Answer:
The area of rectangle is Length × Breadth
Step-by-step explanation:
You have already learnt that perimeters of plane figures and areas of squares and rectangles. Perimeter is the distance around a closed figure while area is the part of plane or reason occupied by the closed figure.
[tex] \sf \: Squares \: and \: Rectangles[/tex]
Ananya and samira made pictures. Ananya made her picture on a rectangular sheet of length 60 cm and breadth 20 cm while samira made hers on a rectangular seat of length 40 cm and breadth 35 cm. Both these pictures have to be separately framed and laminated.
Who has to pay more for farming is the cost of farming is $3.00 per cm?
If the cost of lamination is $2.00 per cm², who has to pay more for lamination?
For finding the cost of farming, we need to find perimeter and then multiply it by the rate for farming. For finding the cost of lamination we need to find area and then multiply it by the rate of lamination.
Example:-Find the area of the rectangle whose Length is 4 cm and breadth/width is 6 cm .
Answer:
The area of the rectangle is 24 cm²
Step-by-step explanation:
Length of rectangle = 4 cm
Breadth of rectangle = 6 cm
[tex] \bf \: Formula \: used[/tex]
[tex] \sf \: Area_ { \{Rectangle \}} = Length × Breadth[/tex]
Now put values
[tex] \sf \: Length = 4 cm [/tex]
[tex] \sf \: Breadth = 6 cm[/tex]
[tex] \sf \: Length × Breadth = 4 × 6 \: cm [/tex]
[tex] \sf \implies 24 \: cm \ {}^{2} [/tex]
Always remember if we find area :-
After units like centimetres,metres we always put (²) on these units.
Like :- 26 cm², 56 m ²
In words = Twenty six centimetre square, Fifty six centimetre square
Required Answer :The area of rectangle is 24 cm²
Additional informatioNPerimeter
Parallelogram = 2(Base + Height)Triangle = a + b + cRectangle = 2(Length + Width)Square = 4×sideTrapezoid = Base + Base + side + sideRhombus = 4 × sideHexagon = 6 × sideArea
Square area formula: = side×sideRectangle area formula: = L × BCircle area formula: = πr²Circle sector area formula: = r² × angle / 2.Ellipse area formula: = Axis× Axis × πTrapezoid area formula: = (base + base) × h / 2.Area of a Triangle = A = ½ (b × h)♦ Area of Rectangle
Length × Breadth[tex] \underline{ \rule{140pt}{4pt}}[/tex]
Additional Information :-Area - Region occupied by figure is called area.
[tex] \large \bf{ \mathfrak{{More \: Formulas \: \red{( Area)}}}}[/tex]
[tex] \large \sf \leadsto \: triangle = \frac{1}{2} \times bh[/tex]
[tex]\large \sf \leadsto \: \: Rectangle \: = \: lb[/tex]
[tex]\large \sf \leadsto \: \: Square \: = {s}^{2} [/tex]
[tex]\large \sf \leadsto \: \: Parallelogram \: = \: bh[/tex]
[tex]\large \sf \leadsto \: \: Rhombus \: = \: \frac{1}{2} \times \: d1 \times d2[/tex]
[tex]\large \sf \leadsto \: \: Trapezium \: = \frac{1}{2} \times (x + y) \times h[/tex]
[tex]\large \sf \leadsto \: \: Quadrilateral \: = \: \frac{1}{2} \times d(h1 + h2)[/tex]
[tex]\large \sf \leadsto \: Circle \: = {\pi \: r}^{2} [/tex]
[tex]\large \sf \leadsto \: \: Equilateral \triangle \: = \frac{ \sqrt{3} }{4} \times {s}^{2} [/tex]
a population of 1200 farm workers, aged 40-55 years, was examined in february 2000. of these workers, 800 were exposed to high levels of pesticide the rest were exposed to low levels of pesticide. at the physical examination, 230 cases of skin cancer were identified, including 185 cases among the high pesticide exposure group. all of the workers who were initially examined and did not have skin cancer were followed by repeat examinations over the next two years. these follow-up exams identified 175 new cases of skin cancer in the total group, including 25 cases among the low-exposure group. what is the incidence of skin cancer over the two years in the high exposure group?
The incidence of skin cancer over the two years in the high exposure group is 24.39%.
To calculate the incidence of skin cancer over the two years in the high exposure group, follow these steps:
1. Determine the number of workers in the high exposure group: 800 workers
2. Subtract the initial skin cancer cases in the high exposure group from the total number of workers in the group to find out the workers without skin cancer:
800 - 185 = 615 workers
3. Calculate the number of new skin cancer cases in the high exposure group by subtracting the new cases in the low-exposure group from the total new cases:
175 - 25 = 150 cases
4. Calculate the incidence rate by dividing the new cases in the high exposure group by the number of workers without skin cancer in the high exposure group:
150 / 615 ≈ 0.2439
5. Multiply the incidence rate by 100 to express it as a percentage:
0.2439 * 100 = 24.39%.
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What steps should be taken to calculate the volume of the right triangular prism? Select three options. A triangular prism. The triangular base has a base of 8 meters and height of 14 meters. The height of the prism is 7 meters. Use the formula A = one-half b h to find the area of the base. Use the formula A = b h to find the area of the base. The area of the base, A, is One-half (7) (8) = 28 meters squared. The area of the base, A, is One-half (8) (14) = 56 meters squared. The volume of the prism, V is (56) (7) = 392 meters cubed.
Answer:
392
Step-by-step explanation:
Volume is the area of the base times the height.
Area of the base:
[tex]\frac{(8x14)}{2}[/tex] = 56
Volume:
area of the base times the height
(56)(7) = 392
Helping in the name of Jesus.
Mason's mother wants to make 8 curtains that each require 2 1/5 (two, one over five) metres of material in a standard width, but she only has 16 1/4(sixteen, one over four)metres of material. There are to be no seams in her curtains. She asks Mason to buy more material.
a. How much more material must Mason buy?
B. How much material is left over?
The result is negative, meaning there is insufficient material to make the curtains without seams.
EquationsEach curtain requires 2 1/5 meters of material, so for 8 curtains, the total amount of material required is:
8 x 2 1/5 = 17 3/5 meters
However, Mason's mother only has 16 1/4 meters of material, so she needs to buy more material. The amount of additional material needed is the difference between what she has and what she needs:
17 3/5 - 16 1/4 = 1 2/5 meters
Therefore, Mason needs to buy 1 2/5 meters of material.
To determine how much material is left over, we need to subtract the total amount of material needed for the curtains from the amount of material Mason's mother has:
16 1/4 - 17 3/5 = -1 3/20
In this case, Mason's mother would need to either buy more material or adjust the dimensions of the curtains to fit the amount of material she has.
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What is the value of p in the equation shown?
p3
= -0.027
The value of p in the equation shown is 0.3
What is equation?
An equatiοn in writing prοving the similarity οf twο phrases. It is made up οf a series οf characters divided intο left and right sectiοns and cοnnected by an equal sign.
Equatiοns are questiοns, and the search fοr methοdical sοlutiοns tο thοse questiοns has fueled the grοwth οf mathematics. Simple algebraic equatiοns with οnly additiοn οr multiplicatiοn tο differential equatiοns, expοnential equatiοns with expοnential fοrmulas, and integral equatiοns are examples οf variοus types οf equatiοns.
The equation that is in the question is given below
p³ = -0.027
or, p=-∛0.027
or, p = -0.3
Hence the value of the p is 0.3
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Find the x- and y-intercepts of the graph of x+7y=12. State each answer as an integer or an improper fraction in simplest form
The x-intercept is (12, 0) and the y-intercept is (0, 12/7) or (0, 1 5/7) in mixed number form.
What are the intercepts?
Intercepts are the points where the graph intersects either the x-axis or the y-axis. The x-intercept is the point where the graph intersects the x-axis, which means the y-coordinate of the point is 0. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of the point is 0. To find the intercepts of a function, you can set one of the variables (x or y) to 0 and solve for the other variable. The resulting point will be the intercept.
To find the x-intercept, we set y to zero and solve for x:
x + 7(0) = 12
x = 12
So the x-intercept is (12, 0).
To find the y-intercept, we set x to zero and solve for y:
0 + 7y = 12
y = 12/7
So the y-intercept is (0, 12/7) or (0, 1 5/7) in mixed number form.
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Can you pls do this i can't do it, it's a little hard and due before 4:00 pm ( Will mark brainliest if 2 answers and 95 pts if you can do it pls and thank you!!)
Answer:
30%
Step-by-step explanation:
(156-120) / 120 × 100％
=36 / 120 × 100％
=30%
if northwest airlines selects randomly a set of 40 flights on a given day, and then selects randomly a group of ten passengers on each of these flights to participate in an in-flight survey, the passengers are best referred to as a .
The passengers selected for the in-flight survey in this scenario can be best referred to as a stratified random sample.
In stratified random sampling, the population is divided into smaller, non-overlapping groups, called strata, which share similar characteristics. In this case, the strata are the 40 flights selected by Northwest Airlines. From each of these strata, a random sample of passengers is chosen, which in this case, is a group of ten passengers from each flight.
This method ensures that each flight's passengers are represented in the survey, allowing for better generalizability of the results. By selecting passengers randomly within each stratum, the survey helps minimize selection bias and ensures that the sample reflects the diversity of the overall population of passengers. The stratified random sampling approach is especially useful when studying a large and diverse population, as it provides a more accurate representation of the population's characteristics compared to simple random sampling.
In summary, the passengers participating in the in-flight survey are best referred to as a stratified random sample because they are chosen from 40 randomly selected flights, with ten passengers randomly selected within each flight. This sampling approach ensures better representation of the overall population and helps minimize selection bias in the survey results.
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3dm 5dm 2dm to mm is?
3 dm is equal to 300 mm, 5 dm is equal to 500 mm, and 2 dm is equal to 200 mm.
To convert 3 dm to mm, we multiply by 10 to get 30 cm, and then by another 10 to get 300 mm.
To convert 5 dm to mm, we multiply by 10 to get 50 cm, and then by another 10 to get 500 mm.
To convert 2 dm to mm, we multiply by 10 to get 20 cm, and then by another 10 to get 200 mm.
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Can someone please help me ASAP it’s due today!! I will give brainliest if it’s correct.
Answer:
about 7 days
Step-by-step explanation:
31 · .22
6.82 days
rounded up it would be approximately 7 days
100 points!!!
Express the function graphed on the axes below as a piecewise function.
This means that for x values less than or equal to -2, the function equals -2x - 1. For x values between -2 and 1, the function equals x^2 + 2x - 3. And for x values greater than or equal to 1, the function equals 4.
To express the function graphed on the axes below as a piecewise function, we need to analyze the graph and determine the different intervals where the function behaves differently.
Looking at the graph, we can see that the function is a straight line with a slope of 2 when x is less than or equal to -2. Then, the function changes to a parabola that opens upwards when x is between -2 and 1. Finally, the function becomes a horizontal line when x is greater than 1.
Therefore, the piecewise function that represents this graph is:
f(x) =
-2x - 1, if x ≤ -2
x^2 + 2x - 3, if -2 < x < 1
4, if x ≥ 1
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A strawberry patch is 1.7 dam long and 1.4 dam wide. If one person can pick 3 m² of strawberries in an hour, then how many hours will it take for one person to harvest the entire patch?
79 hours will it take for one person to harvest the entire strawberry patch.
What is the conversion of the unit?The same property is expressed using a unit conversion but in a distinct unit of measurement. For instance, time can be stated in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other length unit instead of miles.
Finding the strawberry patch's area in square meters and dividing it by the amount that one person can harvest in an hour will give us the total number of hours needed to solve this issue.
The strawberry patch's measurements must first be changed from decameters (dam) to meters.
1 decameter (dam) = 10 meter
Strawberry patch length in meters = 1.7 dam * 10 m/dam = 17 m.
The strawberry patch width in meters = 1.4 dam x 10 m/dam = 14 m.
The strawberry patch's area is therefore:
Area of strawberry patch = length × width = 17 m × 14 m = 238 m²
We must now determine how long it will take one individual to pick 3 m² of strawberries, in hours. We can calculate this by dividing the patch's overall area by the area that a single individual can select in an hour:
[tex]\frac{Area of strawberry patch}{ Area picked per hour }[/tex] = a number of hours needed to harvest the complete patch.
The total harvesting time is [tex]\frac{238 m2 }{3 m2/hour}[/tex] = 79.33 hours nearly equal to 79
Therefore, it would take one person 79 hours to gather the complete strawberry patch.
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Find the inverse of the function.
y = x² + 4x + 4
y =
1
-X+2
2
1
y=± √ √=x+2
Oy=± √√x-2
y = √√x -2
To find the inverse of the function y = x² + 4x + 4, we first replace y with x and x with y:
x = y² + 4y + 4
Next, we rearrange the equation to isolate y on one side of the equation:
x - 4 = y² + 4y
y² + 4y = x - 4
Now, we complete the square by adding (4/2)² = 4 to both sides of the equation:
y² + 4y + 4 = x
We can rewrite the left side of the equation as (y + 2)²:
(y + 2)² = x
Finally, we take the square root of both sides of the equation and solve for y:
y + 2 = ±√x
y = ±√x - 2
Since the original function is not one-to-one, we need to restrict the domain to obtain the inverse function. Specifically, we restrict the domain of the original function to x ≥ -2, since for values of x less than -2 there are two corresponding y-values. Therefore, the inverse function of y = x² + 4x + 4 for this restricted domain is:
y = ±√x - 2, x ≥ -2
PLS HELPP I NEED ASAP
Answer:
Let's call the number of nuts "n", the number of bolts "b", and the number of screws "s".
From the problem, we know:
s = 3n (Since there are 3 times as many screws as nuts)
b = n + 32 (Since there are 32 more bolts than nuts)
n + s + b = 782 (Since the total number of nuts, screws, and bolts is 782)
Now we can use substitution to solve for one of the variables in terms of the others. Let's solve for "n":
n + 3n + (n + 32) = 782
5n + 32 = 782
5n = 750
n = 150
Now we know there are 150 nuts. We can use this information to find the number of bolts:
b = n + 32
b = 150 + 32
b = 182
Finally, we can use the information we have about the screws to find their number:
s = 3n
s = 3(150)
s = 450
Therefore, there are 450 screws in the box.
answer 1646
let nuts be-782
screw=3X nuts
bolts = 32 X nuts
Screw=3x782=1646
hope this helps
can I have the answer? It’s for completing the square
So, the equation of the given curve is a circle centered at (-13, 13) with a radius of 3. Therefore, the correct option is:
[tex](x + 13) ^ 2 + (y - 13) ^ 2 = 9[/tex].
What is equation?An equation is a mathematical statement that shows the equality between two expressions, typically separated by an equal's sign (=). Equations are used to represent a wide range of mathematical and scientific relationships, such as physical laws, chemical reactions, and statistical models. The expressions on either side of the equals sign can contain variables, constants, and mathematical operations, and solving the equation involves finding the value or values of the variables that make the equation true. Equations can take many forms, including linear equations, quadratic equations, trigonometric equations, and differential equations, among others.
To determine which option is correct, we can try to convert the given equation to the standard form of the equation of a circle, which is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
where (h, k) is the center of the circle and r is the radius.
We can complete the square for the given equation by adding and subtracting appropriate constants:
[tex]x^2 + 26x + y^2 - 26y + 329 = 0[/tex]
[tex](x^2 + 26x + 169) + (y^2 - 26y + 169) = -329 + 2(169)[/tex]
[tex](x + 13)^2 + (y - 13)^2 = 9[/tex]
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I need help please!!
Answer:
8 = 83°
Step-by-step explanation:
4 = 2 (Vertically opp. angles)
2 = 8 (Alternate interior angles)
Therefore 4 = 8
Since 4 = 83°
8 = 83°
Answer:
<8 = 83 degrees
Step-by-step explanation:
<4 and <8 are corresponding angles and corresponding angles are equal if lines are parallel
<4 = 83 so <8 = 83
7x-22 is the bottom
3x+10 is the side
wart is a rhombus find WA
x=
WA=
Answer:
x = 8WA = 34Step-by-step explanation:
You want the value of x and the length of side WA in rhombus WART with sides marked 7x-22 and 3x+10.
RhombusThe sides of a rhombus are congruent, so ...
7x -22 = 3x +10
4x = 32 . . . . . . . . add 22-3x
x = 8
3x+10 = 3·8 +10 = 34
The value of x is 8, and side WA is 34 units.
Line segment AB has endpoints A(1, 4) and B(4. 2j. Find the coordinates of the point that divides the line segment directed from A to B
in the ratio of 1:4
The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4 is (8/5, (16 + 8j)/5).
We can use the ratio formula for finding the coordinates of the point that divides the line segment AB in the ratio of 1:4:
Let the coordinates of the point dividing the line segment AB be (x, y). Then:
x = (41 + 14)/5 = 8/5
y = (44 + 42j)/5 = (16 + 8j)/5
Therefore, the coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8/5, (16 + 8j)/5).
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A=1\3+1\6+1\10+1\15+...+1\45
The value of A is 9/10.
What is binomial?
Binοmial refers tο a type οf prοbability distributiοn that describes the number οf successes in a fixed number οf independent trials, where each trial has οnly twο pοssible οutcοmes (success οr failure) and the prοbability οf success is cοnstant acrοss all trials.
The given expressiοn is the sum οf the first several terms οf a harmοnic series. Tο evaluate it, we can use the fοrmula fοr the sum οf the first n terms οf a harmοnic series:
1 + 1/2 + 1/3 + ... + 1/n = ln(n) + γ,
where ln(n) is the natural lοgarithm οf n and γ is the Euler-Mascherοni cοnstant (apprοximately 0.5772).
Using this fοrmula, we can write the expressiοn as:
A = 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/45
= (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ... + (1/9 - 1/10)
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10
= 1 - 1/10
= 9/10
Therefore, the value of A is 9/10.
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Complete Question:
Find The value of A
A=1\3+1\6+1\10+1\15+...+1\45
at the town flea market, monica purchases a big box of used tennis balls to throw to her dog. she scoops some tennis balls out of the box at random. here are the colors of the balls: yellow, blue, yellow, red, green, blue, yellow, red, yellow, green, yellow, red, green based on the data, what is the probability of choosing a yellow tennis ball from the box? write your answer as a fraction or whole number. submit
Answer: 5/13
Step-by-step explanation: i did this IXL and got it right
jenny chagrined to find that the ratio of dandelions to peonies in the garden was 12 to 5 if there were 45 peonies in the garden how many dandelions were there?
Accοrding tο the ratiοs, there are 108 dandeliοns in the garden.
What is a ratiο?A ratiο is a cοmparisοn οf twο quantities οr values, οften expressed as a fractiοn. Ratiοs can be used tο express the relatiοnship between twο οr mοre quantities.
We can use the ratiο οf dandeliοns tο peοnies tο find the number οf dandeliοns when we knοw the number οf peοnies.
The ratiο οf dandeliοns tο peοnies is 12 tο 5, which means that fοr every 12 dandeliοns, there are 5 peοnies.
We knοw that there are 45 peοnies in the garden, sο we can set up a prοpοrtiοn tο find the number οf dandeliοns:
12/5 = x/45
Tο sοlve fοr x, we can crοss-multiply and simplify:
12*45 = 5x
540 = 5x
x = 108
Therefοre, there are 108 dandeliοns in the garden.
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sorry! earn 10 points.
Solve the expression 9 + (20 x one-fourth) – 6 ÷ 2 using PEMDAS.
8
11
13
16
The value of the expression 9 + (20 x one-fourth) – 6 ÷ 2 is 11.
What is PEMDAS?
PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It is a mnemonic or acronym used to remember the order of operations when simplifying mathematical expressions.
Using PEMDAS (Order of Operations), we perform the operations in the following order:
Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Applying this to the given expression:
9 + (20 x one-fourth) – 6 ÷ 2
= 9 + (20 x 0.25) - 3 [simplify division first: 6 ÷ 2 = 3]
= 9 + 5 - 3 [simplify multiplication: 20 x 0.25 = 5]
= 11 [simplify addition and subtraction from left to right]
Therefore, the value of the expression is 11.
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Briony needs 8 pieces of curtain material 2 1/4m in length.She has 19 m length of material does she have enough
Yes, Briony has enough material. She needs 18m of material, which is less than the 19m she has.
To find length of material, we need to calculate the length of each
curtain piece using the given length of material.
To convert a mixed number to an improper fraction, multiply the
denominator (the bottom number) by the whole number, and add the
numerator (the top number).
Now, to convert 2 1/4m into an improper fraction, we multiply the
denominator (4) by the whole number (2), then add the numerator (1).
This gives us (2 × 4) + 1 = 9.
Hence, 2 1/4m can be written as 9/4m.
Since Briony needs 8 pieces of curtain material 2 1/4m in length, she will need a total of:
8 × 2 1/4m = 8 × 9/4m = 18 1/4m.
Briony requires 18 1/4m of curtain material. Since she has 19 m length of
material, she has enough to create 8 pieces of curtain material of 2 1/4m
in length.
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many clothing stores use mannequins to display their goods, with many stores using headless mannequins while some use mannequins with a head. the same dress was presented to 95 women on either a mannequin with or without a head. 18 of the 50 women who saw the dress on a mannequin with a head indicated they would purchase the dress while 12 of the 45 who saw the dress on a headless mannequin said they would purchase the dress. is this evidence that a headed mannequin is more effective in selling clothing? perform a hypothesis test.
Using the hypothesis test, the p-value is greater than the significance level, we fail to reject the null hypothesis. There is not enough evidence to suggest that a headed mannequin is more effective in selling clothing.
To perform a hypothesis test to determine if a headed mannequin is more effective in selling clothing, we can use a two-sample proportion test.
Let p1 be the proportion of women who would purchase the dress when presented on a mannequin with a head, and p2 be the proportion of women who would purchase the dress when presented on a headless mannequin.
The null hypothesis is that there is no difference between the two proportions, i.e. p1 = p2, and the alternative hypothesis is that p1 > p2 since we want to test if the headed mannequin is more effective.
We can use a significance level of 0.05. Using the given data, we calculate the test statistic as:
z = (p1 - p2) / √(p × (1-p) × (1/n1 + 1/n2))
where p = (x1 + x2) / (n1 + n2), x1 = 18, x2 = 12, n1 = 50, and n2 = 45.
The calculated z-value is approximately 1.02.
Using a standard normal distribution table, we find the p-value to be approximately 0.155.
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Can someone please help
The total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 1/36 = 0.028
What is probability?The likelihood that a specific occurrence will occur.
The proportion of the total number of possible outcomes to the number of outcomes in an exhaustive set of equally probable outcomes that result in a particular event.
Two six-sided dice are rolled there are 36 possibilities for outcomes which means 6 possibilities for the first dice and 6 for the second dice.
Therefore 36 is the total possibility outcome.
Count the number of outcomes for the one dice show 5 and the second dice show 6.
There is only one possibility two show the (5, 6) from the total s3 outcomes.
so the probability of rolling a 5 and a 6 i = 1/36 or about 0.028.
Therefore, the total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 1/36.
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56% of what number is $21.84?
Percent Proportion-
Percent Equation -
Answer: 39
Step-by-step explanation:
x = (56/100) * y
where x is the amount we're trying to find and y is the total amount.
We're given that 56% of this value is $21.84, so we can substitute these values into the equation:
21.84 = (56/100) * y
To solve for y, we can divide both sides by 56/100:
y = 21.84 / (56/100)
Simplifying this expression, we get:
y = 39
Therefore, the number that represents 56% of this value is $21.84.
y=log(4x-a) for what values of x will the log be positive
The logarithmic function y = log(4x-a) is positive for all values of x which are greater than a/4.
A logarithmic function is what?A function of this type is a logarithmic function. which can be interpreted as "y equals the log, base b, of x" or "y equals the log of x, base b."
Finding the domain of x that makes the argument (4x-a) of the logarithm positive will help us identify the values of x for which the logarithm in the equation y = log(4x-a) is positive.
Remember that a positive number's logarithm is positive and a negative number's logarithm is indeterminate. (in the real number system).
We must therefore identify the x values that meet the inequality:
4x - a > 0
4x > a
x >a/4
After finding x, we obtain:
x > a/4
The equation y = log(4x-a) therefore has the following domain of x for which the logarithm is positive:
In other words, for all values of x larger than a/4, the expression y = log(4x-a) is defined and positive.
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pls help me, I have to give it in, pls help!!
By algebra properties, the values of x for each equation are listed below:
Case A: x = 0
Case B: x = 0
Case C: x = 1.584 or x = 1
Case D: x = 1.262 or x = - 0.631
Case E: x = 0.569
Case F: x = 2 or x = 1.322
How to solve equations involving exponential expressions
In this problem we find six cases of equations containing exponential expressions where the value of x must be found. This can be done by means of algebra properties:
Case A
2²ˣ - 2 ˣ⁺¹ + 1 = 0
(2ˣ)² - 2 · 2ˣ + 1 = 0
u² - 2 · u + 1 = 0
(u - 1)² = 0
u = 1
2ˣ = 1
x · ㏒₂ 2 = ㏒₂ 1
x = ㏒₂ 1
x = 0
Case B
3²ˣ - 3ˣ = 0
(3ˣ)² - 3ˣ = 0
3ˣ · (3ˣ - 1) = 0
3ˣ - 1 = 0
3ˣ = 1
x = 0
Case C
2²ˣ - 5 · 2ˣ + 6 = 0
(2ˣ)² - 5 · 2ˣ + 6 = 0
u² - 5 · u + 6 = 0
(u - 3) · (u - 2) = 0
u = 3 or u = 2
2ˣ = 3 or 2ˣ = 2
x = ㏒₂ 3 or x = 1
x = 1.584 or x = 1
Case D
2 · (3²ˣ) - 9 · 3ˣ + 4 = 0
2 · u² - 9 · u + 4 = 0
2 · [u² - (9 / 2) · u + 2] = 0
2 · (u - 4) · (u - 1 / 2) = 0
u = 4 or u = 1 / 2
3ˣ = 4 or 3ˣ = 1 / 2
x = ㏒₃ 4 or x = ㏒₃ (1 / 2)
x = 1.262 or x = - 0.631
Case E
6 · (5²ˣ) - 11 · 5ˣ - 10 = 0
6 · u² - 11 · u - 10 = 0
6 · [u² - (11 / 6) · u - 5 / 3] = 0
6 · (u - 2.5) · (u + 0.667)
u = 2.5 or u = - 0.667
x = 0.569
Case F
2²ˣ⁺¹ - 13 · 2ˣ + 20 = 0
2 · (2ˣ)² - 13 · 2ˣ + 20 = 0
2 · u² - 13 · u + 20 = 0
2 · [u² - (13 / 2) · u + 10] = 0
2 · (u - 4) · (u - 5 / 2) = 0
u = 4 or u = 5 / 2
2ˣ = 4 or 2ˣ = 5 / 2
x = 2 or x = 1.322
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Mrs. Simcox needs to make snickerdoodles for her class for Pi day. She needs 2 ¼ cups flour for each batch of cookies. If she has 9 cups of flour how many complete batches of cookies can she make?
Hellpppp
Mrs. Simcox can make 4 complete batches of snickerdoodles for her class on Pi day, as she has 9 cups of flour and each batch of cookies requires 2 and 1/4 cups of flour.
Mrs. Simcox needs to make snickerdoodles for her class on Pi day and she knows that each batch of cookies requires 2 and 1/4 cups of flour. Therefore, she needs to calculate how many batches of cookies she can make with the 9 cups of flour that she has.
To do this, she divides the total amount of flour she has (9 cups) by the amount of flour required for each batch (2 and 1/4 cups). To simplify this division, she can convert the mixed number (2 and 1/4) to an improper fraction:
2 and 1/4 = (2 x 4 + 1)/4 = 9/4
Therefore, she can rewrite the division as:
9 cups ÷ 9/4 cups per batch
To divide by a fraction, she can multiply by its reciprocal:
9 cups × 4/9 cups per batch = 4 batches
So, Mrs. Simcox can make 4 complete batches of cookies with the 9 cups of flour she has.
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select all of the expressions that are equivalent to 4√5
2√20
6^1/2- 5^1/2
3 x 5^1/2 +5^1/2
4 x 5^1/2
2√10
3 x 5^1/2
The expressions that are equivalent to 4√5 is
A) 2√20
C) [tex]3\sqrt5+\sqrt5[/tex]
D) [tex]4\times 5^{1/2}[/tex]
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here the given expression is [tex]4\sqrt5[/tex].
Now simplifying the given option expressions then,
A) [tex]2\sqrt{20}[/tex] = [tex]2\sqrt{4\times5}[/tex]
= [tex]2\times2\sqrt{5}[/tex]
= [tex]4\sqrt5[/tex]
B) [tex]6^{1/2}-5^{1/2}[/tex]
[tex]= \sqrt6-\sqrt5[/tex]
C) [tex]3\sqrt5+\sqrt5[/tex]
= [tex]4\sqrt5[/tex]
D) [tex]4\times 5^{1/2}[/tex]
[tex]= 4\sqrt5[/tex]
E) [tex]2\sqrt{10}[/tex]
F) [tex]3\times5^{1/2}[/tex]
[tex]=3\sqrt5[/tex]
Hence the expressions that are equivalent to 4√5 is
A) 2√20
C) [tex]3\sqrt5+\sqrt5[/tex]
D) [tex]4\times 5^{1/2}[/tex]
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Mr ABA class is making 200 origami cranes for an art project so far they have made 3/4 of the cranes
B. What percent of the cranes have they made?
Step-by-step explanation:
To find the percentage of a fraction you divide the top by the bottom and multiply by 100. So 3/4 = 0.75 then 0.75 x 100 = 75%. Now you need to find 3/4ths or 75 percent of 200. An easy way to do this is find 1/4 of 200. So 200/4 = 50. Now you need 3/4 of 200, not just one fourth so multiply 50 by 3 to get 150. The class has made 150 cranes.