a). The number of scores which are expected to be lower than 18.31 is; 16 scores.
b). The number of scorers that are expected to be below 32.38 is; 98 scores.
Calculations involving normal distribution.As evident in the task content; the 100 ACT scores in discuss are normally distributed, hence, all peculiar characteristics of a normal distribution apply.
First, since the mean is given as; 23 and the standard deviation is; 4.69.
By observation; 23 - 4.69 = 18.31 and
23 + 4.69 + 4.69 = 32.38.
a). Since the percentage of data values which fall below one standard deviation below the mean is; 15.9% which is approximately; 16%.
Therefore, the number of scores below the 18.31 score is; 16% of 100 = 16 scores.
b). Also, since the score; 32.38 is 2 standard deviations above the mean, and it follows from a normal distribution that the percentage of data values below such data value is; 97.7% which is approximately 98%.
Therefore, the number of scores which are expected to be below 32.38 is; 98% of 100 = 98.
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What are the coordinates of point G?
Answer:
D. (4,9)
Step-by-step explanation:
Solve the system of linear equations by graphing. Y=-3 and 6x +y=3
a gold and diamond bracelet sells for $1800 . find the sales tax and the total price if the sales tax rate is 5.5% .
Answer:
Sales Tax In Amount =$99
Total amount of purchase = $1899
Step-by-step explanation:
First, let's find sales tax price in amount(dollars)
(Total Amount)*(percentage of tax)/100=Tax in amount
(1800)*(5.5%)/100 = $99
Therefore, the sales tax in amount would equal to $99, which is the same as 5.5%.
Now, let's find the total price of the purchase.
$1800+$99= $1899
So, the total cost of the purchase would equal to $1899.
The price of the gold bracelet after adding sales tax is $1899 and sale tax is $99.
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Given that, the original price of a gold bracelet is $1800 and there is a sales tax of 5.5% on it,
Sales tax = 5.5% of 1800
= $99
The total price = 1800 + 99 = $1899
Hence, The price of the gold bracelet after adding sales tax is $1899 and sale tax is $99.
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Choose the mathematical sentence that most accurately expresses the
information in the problem, and would be most helpful in solving it.
There are 25 milligrams of sodium per serving in a bag of potato chips. In
that bag there are 5 servings. How many milligrams of sodium are there in the
whole bag?
A. S+5 = 25
B. 5 : s= 25
C. S-5 = 25
D. s = 5(25)
O E. S : 5 = 25
O F. S = 25+ 5
Answer:
[tex]s = 5 * 25[/tex]
Step-by-step explanation:
Given
[tex]Servings = 5[/tex]
[tex]Sodium/Serving = 25mg[/tex]
Required
The number of sodium mg in the bag
This is calculated as:
[tex]s = Servings * Sodium/Serving[/tex]
[tex]s = 5 * 25[/tex]
Hence: (D) is correct
What do you say back to someone who said: “ Nobody understands how it is to be everyone’s go to and have no one to care for you. “?
Answer: just be positive
Step-by-step explanation:
if someone takes your food is it still sharing
Answer:
not unless you want them to have it :)
Step-by-step explanation:
Solve for the value of c (2c-4) (5c+3)
Answer:
its 13
Step-by-step explanation:
An electronics company can spend no more than $4,000 on raw materials for circuit boards. The raw materials cost $10 per ounce for copper and $20 per ounce for silver.
To summarize the situation, a worker writes the inequality:
10c+20s≤4,000 where c is the number of ounces of copper material and s is the number of ounces of silver material.
Which graph's shaded region shows the possible combinations of raw materials the company can buy?
The given graph's shaded region shows the possible combinations of raw materials the company can buy.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
An electronics company can spend no more than $4,000 on raw materials for circuit boards.
And, The raw materials cost $10 per ounce for copper and $20 per ounce for silver.
Here, The inequality for the given condition is,
⇒ 10c + 20s ≤ 4,000
Where, c is the number of ounces of copper material and s is the number of ounces of silver material.
So, The given graph's shaded region shows the possible combinations of raw materials the company can buy.
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You deposit $250 in an account that earns simple interest at an annual rate of 2.2%.
How much money is in the account after 4 years?
Answer: $272
Step-by-step explanation: you would multiply 250 * 0.022 = 5.5
then you would multiply 5.5 * 4 = 22 then you would add 22 + 250 = 272
What is the probability of tossing a coin and getting heads three times in a row?
What is the chance that the next toss will be heads? What is the chance that the next toss will be tails?
The probability of tossing 3 heads in a row is P = 0.125, and after that, because the events are independent, the probability of getting heads (or tails) still is p = 0.5
How to find the probability?Assuming that we have a fair coin, we assume that both outcomes have the same probability, so:
P(tails) = 0.5
P(heads) = 0.5
Then the probability of getting heads 3 times in a row, is the product of the probability of getting heads 3 times, this will be:
P(3 heads) = 0.5*0.5*0.5
P(3 heads) = 0.5^3
P(3 heads) = 0.125
Now, after this point, what is the probability of getting heads or tails?
Remember that each toss of the coin is independent of the previous one, so the probability of getting tails still is 0,5, and the same for the probability of getting heads.
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HELP MEEEEEE PLEASESEE PLEASE
Answer:
240 grams
Step-by-step explanation:
720-480=240
Answer:
240
Step-by-step explanation:
subtraction
720-480
A principal of $3600 is invested at 3.5% interest, compounded annually. How much will the investment be worth after 12 years? Use the calculator provided and round your answer to the nearest dollar. X S
Answer:
$5043
Step-by-step explanation:
To find the value of the investment after 12 years, you can use the following formula:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = principal
r = interest rate
n = number of times the interest is compounded per year
t = number of years
Plugging in the values from the problem, we get:
A = 3600 * (1 + 3.5/100)^(1*12)
Solving this equation, we get:
A = $5043.33
So, after 12 years, the investment will be worth $5043.33.
PlEASE HELP ME WITH TWO QUESTIONS!!!!!!!!!!!
Answer:
3000x5
Step-by-step explanation:
-5(6x+3y-1)
Simplify
Answer:
-30x+15y+5 is the simplified answer
PLEASE HELP AND ANSWER THE QUESTION
Find the distance around each figure. Use 3.14 for pi. 5 feet for radius
Answer:
C≈31.42ft
Step-by-step explanation:
Solution
C=2πr=2·π·5≈31.41593ft
I need help pls answer
need help solving this problem please
Step-by-step explanation:
[tex] \cos( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } \\ = \sqrt{ \frac{1 - ( - \frac{15}{17}) }{2} } \\ = \sqrt{ \frac{32}{34} } [/tex]
6x(2x+3)+1(2x+3)
Rewrite the expression
100 POINTS!!!!! PLEASE HELP!
Answer:
[tex]a^{12} b^{4}[/tex]
Step-by-step explanation:
To simplify we will have to use the negative exponent rule and the power rule along with some algebra.
Negative Exponent Rule
[tex]a^{-b} =\frac{1}{a^b}[/tex]
Power Rule
[tex](a^b)^{c} =a^{bc}[/tex]
Given
[tex](a^{-4}b^{-1}c )^{2} (a^2bc)^{2}[/tex]
Rewrite [tex]a^{-4}[/tex] using negative exponent rule.
[tex](\frac{1}{a^{4}}* b^{-1}c )^{2} (a^2bc)^{2}[/tex]
Rewrite [tex]b^{-1}[/tex] using negative exponent rule.
[tex](\frac{1}{a^{4}}* \frac{1}{b}*c )^{2} (a^2bc)^{2}[/tex]
Simplify
[tex](\frac{c}{a^4b} )^{2} (a^2bc)^{2}[/tex]
Rewrite the base as its reciprocal.
[tex](\frac{a^4b}{c} )^{2} (a^2bc)^{2}[/tex]
Apply the power rule.
[tex]\frac{a^8b^2}{c^2} *(a^2bc)^{2}[/tex]
Apply the power rule.
[tex]\frac{a^8b^2}{c^2} *a^4b^2c^2[/tex]
Cancel the common factor of [tex]c^2[/tex].
[tex]a^8b^2 a^4b^2[/tex]
Apply the power rule.
[tex]a^{12} b^{4}[/tex]
Answer:
[tex]a^{12}\:b^{4}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left(a^{-4}\:b^{-1}\:c\right)^{-2}\left(a^2\:b\:c\right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies a^{(-4 \times -2)}\:b^{(-1 \times -2)}\:c^{-2}\:a^{(2 \times 2)}\:b^2\:c^2[/tex]
Simplify:
[tex]\implies a^{8}\:b^{2}\:c^{-2}\:a^{4}\:b^2\:c^2[/tex]
Collect like terms:
[tex]\implies a^{8}a^{4}\:b^{2}b^2\:c^{-2}c^2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies a^{(8+4)}\:b^{(2+2)}\:c^{(-2+2)}[/tex]
Simplify:
[tex]\implies a^{12}\:b^{4}\:c^{0}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]
[tex]\implies a^{12}\:b^{4}(1)[/tex]
[tex]\implies a^{12}\:b^{4}[/tex]
I need help with this question please help me with this
By basic algebra, the part to be cut is equal to 17/45. When the numerator exceeds or is equal to the denominator, the fraction is said to be improper. 5/2 and 8/5, for instance, are improper fractions. Each fraction has two components.
In math, what is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Let x part is cut to shorten
then,
[tex]\frac{3}{2}-x=\frac{2}{9}\\\\x=\frac{3}{5} -\frac{2}{9} \\\\x=\frac{17}{45}[/tex]
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PS lies on the perpendicular bisector of QR. Select all the statements about the figure that must be true.
Of the given statements, only the option number {5} and {6} are true.
What is perpendicular bisector?The perpendicular bisectors of a triangle are lines passing through the midpoint of each side which are perpendicular to the given side. A triangle's three perpendicular bisectors meet at a point. known as the circumcenter, which is also the center of the triangle's circumcircle.
Given is a triangle as shown in the image.
Since PS is the perpendicular bisector of QR, we can write -
QS = SR
6n + 3 = 4n + 11
2n = 8
n = 4
QR = QS + SR
QR = 6n + 3 + 4n + 11
QR = 10n + 14
QR = 10 x 4 + 14
QR = 54
and
SR = 4n + 11
SR = 16 + 11
SR = 27
Therefore, of the given statements, only the option number {5} and {6} are true.
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Determine a system of linear equations that represents the problem. Be sure to explain how you created the equations.
Answer:
a-
3x+3y=11.25
4x+2y=10
summarize how you can find the slope of a perpendicular line.
Since "slope" tells us the angle of the line being graphed, the word "slope" is commonly used in mathematics.
Planar geometry states that all lines have slopes. Any slope can be calculated by comparing it to another line, usually the x-axis. A line's slope, or angle, in relation to that x-axis value is how steep it is.
In mathematics, slope is the proportion of the change in the y value to the change in the x value.
Two perpendicular lines have a slope such that the reciprocal of the negative slope of one line equals the slope of the other. The slope of perpendicular lines is -1 as a result.
The relationship between the slopes of parallel lines can be demonstrated using the formula m1.m2 = -1, if the slopes of the two perpendicular lines are m1, m2.
Like a fraction, a slope works by favoring the rise, up-and-down movement, over-the-run, or side-to-side movement. If a line rose up one unit for every rightward unit traveled, the slope would be a positive one.
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In major need of help ‼️
Given: 140 students have I-Phones
Find: How many students have other types of phones
Variable: Independent variable- Survey, Dependent variable- Types of phones
Equation: 140 divided by 4
Solution: is
4/140
4/14= 3
4/20= 5
4/140 = 35
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I just want to write this just in case (you dont have to read this) Many people like myself have alot of problems with math, its really hard! Just keep on trying, I know that everybody says that but please take it into consideration. Work hard, have a nice day!
A cylindrical paint can has a diameter of 12 centimeters and
height of 16 centimeters. Which is closest to the volume of
the paint can in cubic centimeters?
Answer:
Step-by-step explanation:
you could find the area of the circle , then multiply that by the height
area of circle = [tex]\pi[/tex][tex]r^{2}[/tex]
[tex]\pi[/tex][tex]6^{2}[/tex]=113.0973355
16*113.0973355=1809.5573
The volume of the paint can in cubic centimeters 1808.64 cm³.
what is Volume?The amount of space occupied by a three-dimensional figure as measured in cubic units.
given: radius= 6cm and height= 16 cm
Volume of cylinder= πr²h
= 3.14*6*6*16
= 1808.64 cm³
Thus, the volume of the paint can in cubic centimeters 1808.64 cm³.
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please help!
Use the Fundamental Counting Principle to determine how many kinds of teddy bears you can build if you must choose one of each category.
1) Choose the bear.
2) Choose an accessory.
3) Choose sound option.
Answer:
Step-by-step explanation:
33
A quadrilateral with 4 congruent sides and 4 right angles is?
I thought of a number, added 26 to it, and then divided the result by 20. What is my number?
Answer:
12?
Step-by-step explanation:
Two car dealerships pay their employees a monthly salary plus a commission on cars that they sell.
The person who is right on the dealership that pays a higher commission, is Tyson because Dealership A pays the higher commission.
How to find the commission paid ?The commission paid on Dealership A cars can be found by the formula :
= ( Monthly income for 4 cars - Monthly income for 1 car ) / Difference in number of cars
= ( 3, 850 - 1, 900 ) / ( 4 - 1 )
= $ 650
The commission paid on Dealership B cars would be:
= ( Monthly income for 4 cars - Monthly income for 1 car ) / Difference in number of cars
= ( 3, 500 - 2, 000 ) / ( 4 - 1 )
= 1, 500 / 3
= $ 500
Dealership A pays the higher commission.
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