Answer:
Length of AC = 4.5
Length of DB = 4.5
Slope of AC = [tex]-\frac{1}{2}[/tex]
Slope of DB = 2
Classification: Square
Hope this helps!
If 3,000 bacteria, with a growth constant (k) of 2.8 per hour, are present at the beginning of an experiment, in how many hours will there be 15,000 bacteria?
Given:
Initial number of bacteria = 3000
With a growth constant (k) of 2.8 per hour.
To find:
The number of hours it will take to be 15,000 bacteria.
Solution:
Let P(t) be the number of bacteria after t number of hours.
The exponential growth model (continuously) is:
[tex]P(t)=P_0e^{kt}[/tex]
Where, [tex]P_0[/tex] is the initial value, k is the growth constant and t is the number of years.
Putting [tex]P(t)=15000,P_0=3000, k=2.8[/tex] in the above formula, we get
[tex]15000=3000e^{2.8t}[/tex]
[tex]\dfrac{15000}{3000}=e^{2.8t}[/tex]
[tex]5=e^{2.8t}[/tex]
Taking ln on both sides, we get
[tex]\ln 5=\ln e^{2.8t}[/tex]
[tex]1.609438=2.8t[/tex] [tex][\because \ln e^x=x][/tex]
[tex]\dfrac{1.609438}{2.8}=t[/tex]
[tex]0.574799=t[/tex]
[tex]t\approx 0.575[/tex]
Therefore, the number of bacteria will be 15,000 after 0.575 hours.
Look at the drawing below.
(2x +10)
46°
Which equation can be used to determine the value of x?
2x + 10 = 46
2x + 10 + 46 = 180
2x + 10 + 46 = 90
Not Here
Correct answer shall get 10 points hurry pls.
Answer:
[tex]\small\mathfrak\green{2x + 10 + 46 = 180 \: = linear \: pair} \\ \\ \small\mathfrak\red{hope it helps...}[/tex]
Brenda received 3 times as many grades as Robert. Timothy received half as many 85s as Brenda. How many grades of 85 did Brenda, Robert, and Timothy receive altogether?
Answer:
11 grades of 85 did Brenda, Robert, and Timothy receive altogether.
Step-by-step explanation:
Let 6x be the number of 85 received by Brenda.
The number of 85 received by Robert is 1/3 of Brenda= 2x
The number of 85 received by Timothy is 1/2 of Brenda= 3x
Then according to the given conditions
6x+ 2x+ 3x
= 11x
So the number of total 85s received by all the three is 11.
11 grades of 85 did Brenda, Robert, and Timothy receive altogether.
What is the height of the triangle 12 units?
The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.
what is triangle ?
A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.
given
Given, side length, a = 12 units.
the height of equilateral triangle, h = (a√3)/2.
Substituting the value of 'a',
h = (12√3)/2 = 6√3 =
10.39 units.
The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.
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Help
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
3. -2 \leq -2 Subtract 6 from both sides, then 8, and then 2
4. -4 < 8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
The short explanation of the effects of the above operations will not affect the inequality.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9, then we have
4 x 3 x 2 x 4 x 9 < 7 x 3 x 2 x 4 x 9
864 < 1512
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
11 + 3 + (-4) > - 2 + 3 + (-4)
10 > - 3
3. -2 ≤ -2 Subtract 6 from both sides, then 8, and then 2
-2 - 6 - 8 - 2 ≤ -2 - 6 - 8 - 2
- 18 ≤ - 18
4. -4 < 8 Divide both sides by -4, then by -2
- 4 / (-4) > 8 / (-4)
1 / (-2) > - 2 / (-2)
- 1/2 < 1
The short explanation of the effects of the above operations will not affect the inequality.
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You can read 12 pages of a book in 15 minutes.
How many hours will it take you to read a 312-page book?
It will take you 6.5 hours to read a 312-page book
How many hours will it take you to read a 312-page book?From the question, we have the following parameters that can be used in our computation:
Rate = 12 pages of a book in 15 minutes
This means that
Rate = 12 pages/15 minutes
Convert to per hour
Rate = 12 pages/0.25 hour
Evaluate
Rate = 48 pages per hour
For a 312-page book, we have
Time = 312 pages/48 pages per hour
Evaluate
Time = 6.5 hours
Hence, the time is 6.5 hours
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ESSENTIAL QUESTION CHECK-IN
17. Tell how you can determine whether a number is a solution of an
equation.
324 Unit 4
Answer:
Step-by-step explanation:
1. Substitute the number for the variable in the equation.
Rose is fishing from a small boat. A fish swimming at the same depth as the hook at the end of her fishing line is 8 meters away from the hook.
The question is incomplete, as the depth of the hook isn't given in the question. However, using a proposed depth for the hook, we could give a stepwise solution to the exercise.
Answer:
Kindly check explanation
Step-by-step explanation:
If given a hook depth of 6 meters, and a distance of 8 m(fishing line from hook) at the the Same depth, then the distance between rose and the fish, x can be calculated, using the relation.
Hypotenus² = opposite² + adjacent²
(refer to attached picture)
x² = 6² + 8²
x² = 36 +. 64
x² = 100
x = sqrt(100)
x = 10 meters
You can use the actual depth value to obtain the actual solution to your question.
Between which two numbers does the square root of
131 lies?
Answer:
11 and 12
Step-by-step explanation:
this is because the square root of 121 is 11 and the square root of 144 is 12 so the answer will lie between 11 and 12
For what value of k does the pair of linear equations 3x +5y 3 6x KY 8 do not have any solution?
The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 does not have any solution for any value of k.
We can rewrite the equations as:
3x + 5y = 3
6x + ky = 8
To solve this system, we need to eliminate one of the variables. To do this, we can multiply the first equation by 2 and the second equation by -3. This will give us:
6x + 10y = 6
-18x - 3ky = -24
Now we can add the two equations together and get:
-12x - 3ky = -18
Since the coefficient of x is 0, this equation does not have any solution for any value of k.
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Can someone please help me with math.
Answer:
A. 85
Step-by-step explanation:
They are congruent angles, or the same.
Therefore, the answer is 85
A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building.
A right triangle with side length 6 feet, hypotenuse 14 feet, and side h.
In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot.
12.65
Answer:
12.6 ft
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
let h be height up the side of the building , then
h² + 6² = 14²
h² + 36 = 196 ( subtract 36 from both sides )
h² = 160 ( take the square root of both sides )
h = [tex]\sqrt{160}[/tex] ≈ 12.6 ft ( to the nearest tenth )
What is the y-intercept of y= -3x + 6
Answer: 6
Step-by-step explanation:
y = -3x + 6 is the linear equation of the form y = mx + c
where m is the gradient of the graph and c is the y-intercept of the graph.
Hence,
m = -3
c = 6
y-intercept of the graph = c
= 6
The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 1995, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the calendar year in which the number of new cases would reach 887.
The linear regression equation that represents the given set of data is y=0.2x+865.
What is linear regression?Linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables. The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression.
The line of best fit is in the form y=bx+a
The slope is b= [tex]\frac{\sum (x-\bar x)\sum (y-\bar y)}{\sum (x-\bar x)^2}[/tex]
Here, [tex]\bar x[/tex] =(0+1+2+3+4)/5
= 1.8
[tex]\bar y[/tex] = (856+871+924+961+961)/5
= 914.6
∑(x-[tex]\bar x[/tex])=(0-2.5)+(1-2.5)+(2-2.5)+(3-2.5)+(4-2.5)
= -2.5-1.5-0.5+0.5+1.5
= -2.5
∑(y- [tex]\bar y[/tex]) =(865-914.6)+(871-914.6)+(924-914.6)+(961-914.6)+(961-914.6)
= -49.6-43.6+9.4+46.4+46.4
= 9
So, slope b= 1.8×9/9²
b=0.2
Substitute b=0.2 and (0, 865) in y=bx+a, we get
865=0.2×0+a
a=865
Substitute b=0.2 and a=865 in y=bx+a, we get
y=0.2x+865
Therefore, the linear regression equation that represents the given set of data is y=0.2x+865.
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"Your question is incomplete, probably the complete question/missing part is:"
The number of newly reported crime cases in a county in New York State is shown in the accompanying table; where X represents the number of years since 1995, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected number of new cases for 2003, rounded to the nearest whole number: Years since 1995 (x) New Cases (y) 856 871 924 961 961
A jar contains $1.70 in ckels, dimes and quarter. There are twenty coins in all with twice as amny nickels as dimes. How many nickels are there in the jar
American nickels are issued as currency. A value of $1.70 is equal to 10 nickels and 12 dimes ($0.50 + $1.20).
How to find the calculation?A dime is worth ten cents and a nickel five cents. In other words, one dime is equivalent to two nickels.
In light of this, we might state that a nickel is worth half what a dime is worth.
Despite having a higher value than a nickel, the dime is smaller.
n + d = 22 <— d = 22-n
Amount in pennies: 5n + 10d = 170
5n + 10(22 - n) = 170
5n + 220 - 10n = 170
220 - 5n = 170
220 - 170 - 5n = 0
50 - 5n = 0
50 = 5n
n = 10
A value of $1.70 is equal to 10 nickels and 12 dimes ($0.50 + $1.20).
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40% of Damien’s marbles are blue Damien has 30 marbles how many of the marbles are not blue
Answer:
12
Explanation:
40/100 = 0.4
0.4 * 30 = 12
I hope this helps you!
Naomi'sbillforlunchatarestaurantwas$46.Sheleftan18%tip.Whatwastheamountofthetip?
Answer:
$8.28
Step-by-step explanation:
0.18*46=8.28
HELP!!!
Carbon dating is used to determine the age of fossils. A fossil was found with 75% of the original carbon-14. The half-life of carbon-14 is 5,730 years. The equation that models the situation is 0.75=(0.5)x5,730.
How old is the fossil?
Choose the answer that gives the correct logarithmic equation and answer.
A. x≈2,865
B. x≈13,805
C. x≈11,460
D. x≈2,378
help me with this please
Answer:
1)
17/20 will have the same value as 1D.
To get this
given D=1
Substitute that into the equation..
you have
E=17/20
To verify this... input E=17/20 into the original equation to see if you will get 1D
17/20 =17/20D
Multiply through by 20/17
You'll have D=1.
So
17/20E will have the same value as 1U.S dollar.
2)
20/17US dollar will Equal 1E.
Solving arithmetically
Given E=1.
Find D subject
your have
D=20E/17
E=1
D=20/17
To verify this answer
substitute D=20/17 and see if you'll get 1E
E=17/20D
E=17/20 x 20/17
E=1.
Conclusion
20/17D will have the same value as 1E
Making
Jen can bike 12 miles in 40 minutes how much time will she need to bike 30 miles if her speed remains the same
Please help I will mark brainliest
Answer:
100 minutes / [tex]1 \frac{2}{3}[/tex] hours
First, we need to do 40 ÷ 12 = 3 1/3
Next, multiply 3 1/3 by 30 = 100
So, it is 100 minutes. But wait! We can simply it...
100 minutes = 1 2/3 hours
You can always convert it into different time labels. I think this is the most popular.
HELP YOU GUYS THIS IS DUE TODAY AND I WILL MARK BRAINLEST
The answer is yes since there are no repeating x values.
Step-by-step explanation:
Jorge received a 3.1% increase in his pay at work. If he now makes $18.00 per hour, how much was he making before his raise? (Round answer to the nearest cent (hundredths))
Portable telephones can
weigh as little as 8 ounces. How many
pounds is thiS
What are the properties of the graph of a function?
The properties of the graph of a function include domain, range, symmetry, asymptotes, intercepts, increasing or decreasing, continuity, smoothness, behaviour at infinity and shape.
1) Domain: The set of all input values (x-values) that produce a valid output (y-value) for the function.
2) Range: The set of all output values (y-values) that can be produced by the function for any valid input value in the domain.
3) Symmetry: A graph may be symmetric with respect to the x-axis, y-axis, or origin.
4) Asymptotes: A line that the graph of a function gets arbitrarily close to, but never touches.
5) Intercepts: The points where the graph of a function crosses the x- and y-axes.
6) Increasing or Decreasing: A function can be increasing over a certain interval, decreasing over a certain interval, or both.
7) Continuity: A function is continuous if its graph has no breaks or gaps.
8) Smoothness: A function is smooth if its graph has no sharp corners or links.
9) Behavior at Infinity: The behavior of a function at positive or negative infinity can be determined by analyzing the degree and leading coefficient of its equation.
10) Shape: The shape of a graph can be used to classify functions as linear, quadratic, exponential, logarithmic, etc.
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Expand the expression by distributing
-2(-4x-7)
Answer:
8x+14
Step-by-step explanation:
Solve for x: 4 - (x + 2) <-3(x + 4)
OX<-7
Ox>-7
0x=-9
OX-9
Answer:
X < -7
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
"Suppose Dave purchases a puzzle having 650 pieces. Predict the lenght of time it will take him to compleate the puzzle."
a) Attached at the end.
b) Strong positive linear correlation.
c) The length of time is 220 minutes.
What is Scatter plot?A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events, scatter plots are crucial in statistics (called variables).
Given:
a) The Scatter plot Associated with data is attached below.
b) The Scatter plot shows the positive linear correlation between number of pieces in a jigsaw puzzle and time required for a person to complete it.
c) To complete the puzzle with 650 pieces it will take 220 minutes.
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Answer:
a) See attachment.
b) Strong positive correlation.
c) 247 minutes
Step-by-step explanation:
Part aPlot the points from the given table on the given coordinate plane.
Draw a line of best fit.
(See attachment).
Part bAs the line of best fit has a positive gradient, the two variables are positively correlated.
As the line of best fit lies close to most of the points, this indicates there may be a strong correlation.
Part cTo predict the length of time it will take Dave to complete a 650-piece puzzle, locate 650 on the x-axis of the scatter plot, trace up to the line of best fit and read the y-value:
(650, 247)Therefore, it will take Dave approximately 247 minutes to complete a 650-piece puzzle.
take two identical 30°-60°-90° set squares and form a parellelogram as before. Does this figure obtained help you to confirm the above property?
Two identical set squares with angles 30-60-90 degree Placed adjacently to form a parallelogram
The total surface area of a cube is 294 cm".
Work out the volume of the cube.
i would really appreciate it thank you!! :)
Hey Buddy,
Answer:
343 cm³
Step-by-step explanation:
Total Surface Area of the cube = 294 cm²
Surface Area = 6a²
6a² = 294
a² = 49
a = square root of 49
= 7
Volume of a cube = a³
Thus, the volume of the cube = 7³
= 7*7*7
= 343 cubic centimeters
Hope it helps :)
ORIGINAL ANSWERS PLEASE
If the line of best fit is y = 1.18x + 5.4, what is the residual value for the coordinate (2, 8)?
0.24
−0.24
0.46
−0.46
The residual value of coordinate is 0.24.
what is residual?A residual is the discrepancy between a data point's actual value and the value predicted by a regression or trend line.
Trend lines provide the approximate shape of the data and display the general shape the data takes. The most precise trend lines are those that best suit the data.
Given equation y = 1.18x + 5.4
and coordinates (2, 8)
y at x = 2
y = 1.18x + 5.4
y = 1.18(2) + 5.4
y = 7.76
residual value = actual y axis value - predicted y axis value
residual value = 8 - 7.76 = 0.24
Hence the residual value is 0.24.
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