Answer:
49 square inches
Step-by-step explanation:
Length x width =area
since it is a square, all sides have a length of 7 inches
7x7=49 inches ^2
What is the result of a dilation of scale factor 3 centered at the origin of the line 2y + 3x=10?? PLEASE HELP PLEASEEEEEEEEE
Given:
The equation of a line is:
[tex]2y+3x=10[/tex]
The line is dilated by factor 3.
To find:
The result of dilation.
Solution:
The equation of a line is:
[tex]2y+3x=10[/tex]
For [tex]x=0[/tex],
[tex]2y+3(0)=10[/tex]
[tex]2y+0=10[/tex]
[tex]y=\dfrac{10}{2}[/tex]
[tex]y=5[/tex]
For [tex]x=2[/tex],
[tex]2y+3(2)=10[/tex]
[tex]2y+6=10[/tex]
[tex]2y=10-6[/tex]
[tex]2y=4[/tex]
Divide both sides by 2.
[tex]y=\dfrac{4}{2}[/tex]
[tex]y=2[/tex]
The given line passes through the two points A(0,5) and B(2,2).
If the line dilated by factor 3 with origin as center of dilation, then
[tex](x,y)\to (3x,3y)[/tex]
Using this rule, we get
[tex]A(0,5)\to A'(3(0),3(5))[/tex]
[tex]A(0,5)\to A'(0,15)[/tex]
Similarly,
[tex]B(2,2)\to B'(3(2),3(2))[/tex]
[tex]B(2,2)\to B'(6,6)[/tex]
The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-15=\dfrac{6-15}{6-0}(x-0)[/tex]
[tex]y-15=\dfrac{-9}{6}(x)[/tex]
[tex]y-15=\dfrac{-3}{2}x[/tex]
Multiply both sides by 2.
[tex]2(y-15)=-3x[/tex]
[tex]2y-30=-3x[/tex]
[tex]2y+3x=30[/tex]
Therefore, the equation of the line after the dilation is [tex]2y+3x=30[/tex].
mike is looking at the roof of a new house from the front. he notices that the roof is triangular in shape with a base 11.2m. the left side is 6.7m long and makes an angle of 72 degree with the base of the roof. if this is the only known information, determine the angle the right side of the roof makes with the base of the roof to the nearest degree. be sure to first make a sketch
Answer:
35°
Step-by-step explanation:
From the sketch made, to obtain B we use the cosine angle formula :
We have 2 so des and an included angle
Cos B = (a² + c² - b²) / 2ac
First we obtain the side c
c² = a² + b² - 2ab CosC
c² = 11.2² + 6.7² - 2(11.7 * 6.7) * cos 72
c = 11.13
Using the value of c
Cos B = (a² + c² - b²) / 2ac
CosB = (11.2² + 11.13² - 6.7²) / (2*11.2*11.13)
Cos B = 204.4269 / 249.312
B = Cos^-1(204.4269 / 249.312)
B = 34.9°
How many 1/6 cup servings of. Rice are in 2/3 cup of rice
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Answer:
4
Step-by-step explanation:
2/3 = 4/6
There are four 1/6-cup servings of rice in 4/6 cups of rice.
A journal article reports that 34% of fathers take no responsibility for child care. A group of fathers believes that this estimate is too high. In a random sample of 80 fathers, it was found that 23 of those fathers take no responsibility for child care. Is there significant evidence at the 1% significance level that less than 34% of fathers take no responsibility for child care
Answer:
The p-value of the test is 0.1611>0.01, which means that there is not significant evidence at the 1% significance level that less than 34% of fathers take no responsibility for child care
Step-by-step explanation:
A journal article reports that 34% of fathers take no responsibility for child care. A group of fathers believes that this estimate is too high.
At the null hypothesis, we test if the proportion is of at least 34%, that is:
[tex]H_0: p \geq 0.34[/tex]
At the alternative hypothesis, we test if the proportion is less than that, that is:
[tex]H_1: p < 0.34[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.34 is tested at the null hypothesis:
This means that [tex]\mu = 0.34, \sigma = \sqrt{0.34*0.66}[/tex]
In a random sample of 80 fathers, it was found that 23 of those fathers take no responsibility for child care.
This means that [tex]n = 80, X = \frac{23}{80} = 0.2875[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.2875 - 0.34}{\frac{\sqrt{0.34*0.66}}{\sqrt{80}}}[/tex]
[tex]Z = -0.99[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.2875, which is the p-value of Z = -0.99.
Looking at the Z-table, Z = -0.99 has a p-value of 0.1611.
The p-value of the test is 0.1611>0.01, which means that there is not significant evidence at the 1% significance level that less than 34% of fathers take no responsibility for child care
Find the median and mean of the data set below:
10, 43, 20, 11
C. Betsy's dad bought a 5 lb. bag of grass seed. He needed 1 lb. 3 oz. for the front yard, 1 lb. 8 oz. for the side yard, and 2 Ib. 4 oz. for the back yard. Was the 5 lb. bag of seed enough for the three yards?
Explain .___________________________.
Answer:
Yes.
Step-by-step explanation:
When you add the different amounts needed together ( 1lb 3oz + 1lb 8oz + 2lb 4 oz ), you get 4lb 15oz. Since there are 16oz in a pound, you need less than 5 lb. Therefore, you need less than 5lb, the 5lb bag will be more than enough.
Which system of equations represents the matrix shown below?
Answer:
c
Step-by-step explanation:
What would be the correct answer for this
Answer:
The answer is B
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
0.99218
I need help with this question I wanna say the answers B
Answer:
hi, yes the option B is the correct answer
2. The set {0,1,-1} is closed under the operation of?
8,11,14,17 and you have to find the 74th term
Answer:
227 is the 74th term of your question.
Shine has some money in his account.Every Month, he used the same amount of money from his account to pay for his music classes. The table below shows the amount of money left in his account after a certain amount of time, in months:
Option 4) -$45 per month; the amount of money withdrawn per month
Answer:
Option 4) -$45 per month; the amount of money withdrawn per month.
Step-by-step explanation:
The rate of change is 45. Before he began taking money out to pay for his classes[month 0], he had $190. Since then, every month, $45 have been withdrawn.
A college savings account pays 8.2% annual interest compounded semiannually. What is the balance of an account after 12 years if $21,000 was initially deposited?
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Answer:
$55,085.44
Step-by-step explanation:
The formula for the account balance is ...
A = P(1 +r/n)^(nt)
where principal P is invested at annual rate r compounded n times per year for t years. Using the given values, we find the balance to be ...
A = $21,000(1 +0.082/2)^(2·12) = $21,000(1.041^24) ≈ $55,085.44
The balance is $55,085.44 after 12 years.
Find Use proportion
24 =18/15
21
b
18
20
16
Answer:
Step-by-step explanation:
When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information.
Time of Day When Best Ideas Occur
Time Number of Inventors
6 A.M.-12 noon
12 noon-6 P.M.
6 P.M.-12 midnight
12 midnight-6 A.M. 295
138
311
222
Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M. (Enter your answers to 3 decimal places.)
6AM-12PM 12PM-6PM 6PM-12AM 12AM-6AM
Answer:
[tex]P(6am-12\ noon) = 0.305[/tex]
[tex]P(12\ noon - 6pm) = 0.143[/tex]
[tex]P(6pm-12\ midnight) = 0.322[/tex]
[tex]P(12\ midnight - 6am) =0.230[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Time} & {Inventors} & {6am - 12\ noon} & {295} & {12\ noon -6pm} & {138} & {6pm - 12\ midnight} & {311} & {12\ midnight - 6am} & {222} & {Total} & {966} \ \end{array}[/tex]
Required
The probability of each time interval
To do this, we simply divide the number of inventors in the interval by the total inventors (966)
So, we have:
[tex]P(6am-12\ noon) = \frac{6am-12\ noon}{Total}[/tex]
[tex]P(6am-12\ noon) = \frac{295}{966}[/tex]
[tex]P(6am-12\ noon) = 0.305[/tex]
[tex]P(12\ noon - 6pm) = \frac{12\ noon - 6pm}{Total}[/tex]
[tex]P(12\ noon - 6pm) = \frac{138}{966}[/tex]
[tex]P(12\ noon - 6pm) = 0.143[/tex]
[tex]P(6pm-12\ midnight) = \frac{6pm-12\ midnight}{Total}[/tex]
[tex]P(6pm-12\ midnight) = \frac{311}{966}[/tex]
[tex]P(6pm-12\ midnight) = 0.322[/tex]
[tex]P(12\ midnight - 6am) =\frac{12\ midnight - 6am}{Total}[/tex]
[tex]P(12\ midnight - 6am) =\frac{222}{966}[/tex]
[tex]P(12\ midnight - 6am) =0.230[/tex]
Find the equation of a line perpendicular to x+5y=−2 that contains the point (3,0).
Perpendicular Definition:
[tex] \large \boxed{m_1m_2 = - 1}[/tex]
Slopes of two different equations multiply each others and must equal to -1. We can also say that the perpendicular occurs only if both equations are negative reciprocal to each others. For example, we are given the equation of y = 2x. The perpendicular to y = 2x would be y = (-1/2)x. See how both are reciprocal to each others.
From the equation below:
[tex] \large{x + 5y = - 2}[/tex]
Since the equation is in the form of Ax+By = C. It is better to use the another slope formula which is:
[tex] \large \boxed{m = - \frac{A}{B} }[/tex]
From the equation above, use the slope formula to find the slope.
[tex] \large{m = - \frac{1}{5} }[/tex]
Therefore the equation has a slope of -1/5. Next to find the perpendicular equation to the original equation. Since our slope is -1/5 - that means the negative reciprocal of -1/5 is 5. Therefore the slope of perpendicular line is 5.
Next we will be using the point-slope form below:
[tex] \large \boxed{y - y_1 = m(x - x_1)}[/tex]
Given the y1 and x1 or (x1,y1) are the points. Our perpendicular slope is 5 which passes through the point (3,0). Substitute both slope and the point in.
[tex] \large{y - 0 = 5(x - 3)}[/tex]
Simplify in the slope-intercept form as we get:
[tex] \large{y = 5x - 15}[/tex]
Answer
y = 5x-15 is perpendicular to x+5y = -2Hope this helps and let me know if you have any doubts!
Consider two x distributions corresponding to the same x distribution. The first x distribution is based on samples of size n = 100 and the second is based on samples of size n = 225. Which x distribution has the smaller standard error?
Answer:
Hence the correct option is the distribution with n = 225 will have a smaller standard error.
Step-by-step explanation:
Now the standard deviation is
[tex]S.E=\frac{\sigma }{\sqrt{n}}[/tex]
If n = 100 then consider [tex]\sigma =6[/tex]
[tex]S.E=\frac{6}{\sqrt{100}}=0.6[/tex].
If n= 225 then consider [tex]\sigma =6[/tex]
[tex]S.E=\frac{6}{\sqrt{225}}=0.4[/tex].
Here the distribution with n = 225 will have a smaller standard error.
A triangular prism has a base area of 12 square centimeters, and a height of 15 centimeters. What is the volume?
What's 3 times 4/5 as a improper fraction
what is the row of sum 8192 in Pascal's triangle?
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Answer:
row 13
Step-by-step explanation:
The sum of row n is 2^n, so the row number with a particular sum is ...
2^n = sum
n·log(2) = log(sum)
n = log(sum)/log(2)
The row with sum 8192 is ...
n = log(8192)/log(2) = 13
The row of Pascal's triangle that has a sum of 8192 is row 13.
Which graph represents a function with an initial value of One-half?
Answer:
The answer is B
Step-by-step explanation:
I went on socratic and found the answer
Answer:
second graph
Step-by-step explanation:
took the test on edge
[tex]\frac{(csc x+1)(csc x-1)}{csc^2x}\\[/tex]
cscθ·cos^2θ+sinθ= cscθ
Step-by-step explanation:
[tex]\frac{( \csc x+1)( \csc x-1)}{ \csc ^2x} = \frac{ { \csc }^{2} x - 1}{ \csc^{2} x} \\ = 1 - \sin^{2} x = \cos^{2} x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
b. Since csc theta = 1/sin theta, we can multiply both sides by sin theta and you will end up with
[tex] \cos^{2} \theta + \sin^{2} \theta = 1[/tex]
which is an identity.
Need help practice problem please
Answer:
I think there is no solution.
Step-by-step explanation:
Substitute:
Z = -3y-5x+25
X = 3y-2z-13
Put into the last formula:
14(3y-2z-13)-2y+3(-3y-5x+25) = 48
Then:
14(3y-2(-3y-5x+25)-13)-2y+3(-3y-5(3y-2z-13)) = 48
So:
14(3y-2(-3y-5(3y-2z-13)+25)-13)-2y+3(-3y-5(3y-2(-3y-5x+25)-13)) = 48
And so on.
elimination was used to solve a system of equations. one of the intermediate steps led to the equation 2x= 8. which of the following systems could have led to this equation?
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Answer:
C
Step-by-step explanation:
The step shown indicates that y was eliminated from the equations. For choices A, B, D, this is done by adding the equations together (the y-coefficients are opposites). The result of doing that gives x-terms of 4x, 0x, and 0x, respectively. These x-terms do not match the one given: 2x.
For choice C, the y-term is eliminated by subtracting twice the second equation from the first. Doing that gives ...
(4x +2y) -2(x +y) = (14) -2(3)
4x +2y -2x -2y = 14 -6 . . . . eliminate parentheses
2x = 8 . . . . . . . . . . . . . . collect terms
which net represents the pyramid with the greatest surface area
Answer:
the top one that's orange
What is an opposite number?
Answer:
The opposite of a number is the number on the other side of 0 number line, and the same distance from 0.
A stadium's normal ticket price is $78. As a special promotion they offer 15% off. What is the price of the discounted
ticket?
Answer:
$66.3
Step-by-step explanation:
price of a ticket without discount = $78
discount % = 15%
discount amount = ?
price of a discounted ticket = ?
discount amount = discount% of price of a original ticket
=15/100 * $78
=$1170/100
=$ 11.7
price of the discounted ticket = $78 - $11.7
=$66.3
The discounted price of the stadium's normal ticket is $66.3
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A stadium's normal ticket price is $78 and As a special promotion they offer 15% off.
Therefore, The discounted price of the ticket should be (100 - 15)% = 85% of the original price which is,
= (85/100)×78.
= $66.3 is the discounted price.
learn more about percentages here :
https://brainly.com/question/24159063
#SPJ6
GIVING OUT BRAINLIEST HELP MEEE PLSS!!
Answer:
x=7
Step-by-step explanation:
take 30 degree as reference angle
using sin tan rule
tan 30=opposite/adjacent
[tex]\frac{1}{\sqrt{3} }[/tex]=x/[tex]7\sqrt{3}[/tex]
[tex]\frac{1}{\sqrt{3} }[/tex] *[tex]7\sqrt{3}[/tex]
[tex]7\sqrt{3} /\sqrt{3}[/tex]
7=x
A car travels 22 km due south and
then 28 km in a direction 60° east of
south. Find the magnitude of the
car's resultant vector.
Answer:
Step-by-step explanation:
A point particle with charge q is at the center of a Gaussian surface in the form of a cube. The electric flux through any one face of the cube is: _________.
i. q/E0
ii. q/E4Ï€E0
iii. q/4E0
iv. q/6E0
v. q/16E0
Answer:
iv. q/6E0
Step-by-step explanation:
Electric flux formula:
The electic flux formula, of a charge q is given by, through an entire cube, is given by:
[tex]E = \frac{q}{E_o}[/tex]
In which [tex]E_o[/tex] is a constant related to the material.
The electric flux through any one face of the cube is:
Key-word is face, and a cube has 6 faces, with the force distributed evenly throughout it. Thus
[tex]E_f = \frac{1}{6} \times \frac{q}{E_o} = \frac{q}{6E_o}[/tex]
And the correct answer is given by option iv.
