Find the area of the triangle.

[? ] ft2
Don't round

Answer:

The calculated Z= 10/4.61 = 2.169

The P value is 0.975 .

Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.

Step-by-step explanation:

We set up our hypotheses as

H0 : x 1= x2 and Ha: x1 ≠ x2

We specify significance level ∝= 0.05

The test statistic if H0: x1= x2 is true is

Z =  [tex]\frac{x_1-x_2}\sqrt\frac{s_1^2}{n_1}+ \frac{s_2^2}{n_2}[/tex]

Z = 260-250/ √400/50 + 529/40

Z= 10 / √8+ 13.225

Z= 10/4.61 = 2.169

The critical value for two tailed test at alpha=0.05 is ± 1.96

The P value is 0.975 .

It is calculated by dividing alpha by 2 for a two sided test and subtracting from 1. When we subtract   0.025 ( 0.05/2)from 1 we get 0.975

Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.

Answer:

b = - 3.7

Step-by-step explanation:

here are the data values:

x   y          XY        X²

14 46         644       196

15 49         735       225

16 37          592      256

17 42          714        289

18 37          666      324

19 31           589      361

20 25         500      400

21 23          483       441

22 20         440       484

23 15          345       529

24 12         288       576

now we are required to find the summation (total) of all values of X, Y, XY and X².

∑X = 209

∑Y = 337

∑XY = 5996

∑X² = 4081

The formular for finding b is given as:

b = n∑XY - (X)(Y) / n∑X² - (∑X)²

= 11(5996) - (209)(337) / 11(4081) - (209)²

= 65956 - 70433 / 44891 - 43681

= -4477/ 1210

= -3.7

The question asked us to find the value of b but we can  go further to find the equation of the regression line:

a = ∑Y - b∑X / n

= 337 - (-3.7)(209)/  11

=1110.3/11

= 100.94

the equation is:

Y = 100.94 - 3.7X

I hope you find my solution useful!

=

Answer:

The tree grows 33cm per year

Step-by-step explanation:

Here in this question, we are interested in knowing how fast the growth of the tree is.

This is easily obtainable from the equation for the height of the tree.

Mathematically, the equation is given as;

H = 210 + 33t

Interpreting this, we can have 210 as the original height of the tree when Renata moved in, while the term 33 represents the growth per year.

So we can say the tree adds a height of 33 cm each year and this translates to the yearly growth of the tree

This is equivalent to x^2+8x+13

======================================================

Explanation:

The vertex of f is at (0,0). The vertex of g is at (-4, -3). The vertex has moved 4 units to the left and 3 units down.

To shift to the left, we replace x with x+4. So we have f(x) = x^2 turn into f(x+4) = (x+4)^2 so far.

Then we subtract off 3 to move everything 3 units down. We have

g(x) = (x+4)^2-3

---------------------

Optionally we can expand things out like so

g(x) = (x+4)^2-3

g(x) = (x+4)(x+4)-3

g(x) = x(x+4)+4(x+4)-3

g(x) = x^2+4x+4x+16-3

g(x) = x^2+8x+13

Showing that (x+4)^2-3 is equivalent to x^2+8x+13

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

Area of rectangle = l × w

where

l is the length

w is the width

From the question

The length is twice its width is written as

l = 2w

Substitute this into the formula for finding the area of the rectangle

Area = 200 yd²

200 = 2w²

Divide both sides by 2

w² = 100

Find the square root of both sides

width = 10cm

Substitute this value into l = 2w

That's

l = 2(10)

length = 20cm

Perimeter of the rectangle is

2(20) + 2(10)

= 40 + 20

Hope this helps you

Answer:

Step-by-step explanation:

Hello, this is pretty straight forward. Let me remind you the following.

The standard equation of a parabola is

[tex]y=ax^2+bx+c[/tex]

But the equation for a parabola can also be written in "vertex form":

[tex]y=a(x-h)^2+k[/tex]

In this equation, the vertex of the parabola is the point (h,k) .

So, here the vertex is the point (2, -25) and the axis of symmetry is x = 2

Thank you

Answer:

if anyone still needs the answer I added a pic

Step-by-step explanation:

Answer:

Confidence level  = 59.46%

Step-by-step explanation:

Given that:

An economist reports that 576 out of a sample of 1,200 middle-income American households participate in the stock market.

sample mean = 576

sample size = 1200

The sample proportion [tex]\hat p[/tex] = x/n

The sample proportion [tex]\hat p[/tex] = 576/1200 = 0.48

A confidence interval of [0.468, 0.492] was calculated. What confidence level was used in this calculation?

The  confidence interval level can be determined by using the formula:

[tex]M.E =Z_{critical} \times \sqrt{\dfrac{\hat p (1- \hat p)}{n}}[/tex]

If the calculated confidence interval was [0.468, 0.492]

Then,

[tex]\hat p[/tex]  - M.E = 0.468

0.48 -M.E = 0.468

0.48 - 0.468 = M.E

0.012 = M.E

M.E = 0.012

NOW;

[tex]0. 012 =Z_{critical} \times \sqrt{\dfrac{0.48 (1- 0.48)}{1200}}[/tex]

[tex]0. 012 =Z_{critical} \times \sqrt{\dfrac{0.48 (0.52)}{1200}}[/tex]

[tex]0. 012 =Z_{critical} \times \sqrt{\dfrac{0.2496}{1200}}[/tex]

[tex]0. 012 =Z_{critical} \times \sqrt{2.08\times10^{-4}}[/tex]

[tex]0. 012 =Z_{critical} \times 0.01442[/tex]

[tex]\dfrac{0. 012}{0.01442} =Z_{critical}[/tex]

[tex]Z_{critical} =0.8322[/tex]

From the standard normal tables,

the p - value at [tex]Z_{critical} =0.8322[/tex] =  0.7973

Since the test is two tailed

[tex]1 - \alpha/2= 0.7973[/tex]

[tex]\alpha/2= 1-0.7973[/tex]

[tex]\alpha/2= 0.2027[/tex]

[tex]\alpha= 0.2027 \times 2[/tex]

[tex]\alpha= 0.4054[/tex]

the level of significance = 0.4054

Confidence level = 1 - level of significance

Confidence level = 1 - 0.4054

Confidence level = 0.5946

Confidence level  = 59.46%

Answer:

D

Step-by-step explanation:

The true statement is:

The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

As, per the graph and table is:

From the graph of f(x):

Axis of symmetry will be at x = 2

The maximum value of f(x) = 10

From the table of g(x):

Axis of symmetry will be at x = 2

The minimum value of g(x) = 4

thus, The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.

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=========================================

Explanation:

Subtracting a negative is the same as adding. Example: 2-(-3) = 2+3 = 5.

So (x+y)-(-z) is the same as x+y+z. We can group up terms inside parenthesis and it won't change the result. Meaning that x+y+z is the same as any of the following below

We could also swap the order of either x, y or z, and still have the same result.

Answer:

3 1/4

Step-by-step explanation:

Hey there!

Well if Cedarburg to Westford is 8 3/4 miles and Oxford to Westford is 5 1/2 miles, we can make the following,

CO = CW - OW

CO = 8 3/4 - 5 1/2

Make the denominators the same,

5 1/2

improper

11/2

*2

22/4

Proper

5 2/4

8 3/4 - 5 2/4

3 1/4 miles

Hope this helps :)

Answer:

On the map:

0.8 mile / 1.5 inches

=  0.533 mile / 1 inch

Total distance on the map:

0.6 inches

distance travelled in miles:

0.6 * 0.533 = 0.32 miles

please mark brainly if you want

Answer:

The answer is A = 0.3 mile

Step-by-step explanation:

I got it right in 2021.

An apple orchard has an average yield of 32 bushels of apples per tree if tree density is 26 trees per acre. For each unit increase in tree density, the yield decreases by 2 bushels per tree. How many trees per acre should be planted to maximize the yield?

Answer:

Step-by-step explanation:

From the given information:

Let assume that  26+x trees per acre  are planted

then the  yield per acre will be (26+x)(32-2x)

However;

As x = 0 (i.e. planting 26 per acre), we have;

= (26+0) (32 - 2 (0))

= 26 × 32

= 832

As x = 1 (i.e planting 19 per acre), we have:

= (26+1) (32-2(1)

= 27 × 30

= 810

As x = 2 (i.e. planting 20 per acre), we have:

= (26 +2 ) ( 32 - 2(2)

= 28 × 28

= 784

The series continues in a downward direction for the yield per acre.

Thus,  for maximum plant 19 per acre, it can achieved by method of calculus given that the differentiation of the maximum point of x = 1

Finally, due to integer solution, it is not advisable to use calculus as such other methods should be applied.

Answer:

Expression = 2n³ - 20n

Step-by-step explanation:

Find:

Expression

Computation:

Assume given number is 'n'

Cube of number = n³

Twice of cube = 2n³

Subtract number = 20n

Expression = 2n³ - 20n

Answer:

26.75 units²

Step-by-step explanation:

Cube Area: A = l²

Triangle Area: A = 1/2bh

Step 1: Find area of biggest triangle

A = 1/2(3.5)(2 + 2 + 5)

A = 1.75(9)

A = 15.75

Step 2: Find area of 2nd biggest triangle

A = 1/2(5)(2)

A = 1/2(10)

A = 5

Step 3: Find area of smallest triangle

A = 1/2(2)(2)

A = 1/2(4)

A = 2

Step 4: Find area of cube

A = 2²

A = 4

Step 5: Add all the values together

A = 15.75 + 5 + 2 + 4

A = 20.75 + 2 + 4

A = 22.75 + 4

A = 26.75

Answer:

$800

Step-by-step explanation:

Let the original price be $x.

75% reduction ----- 100% -75%= 25%

25%x= 200

[tex] \frac{25}{100} x = 200 \\ x = 200 \div \frac{25}{100} \\ x = 200 \times \frac{100}{25} \\ x = 800[/tex]

Thus, the original price of the clothes dryer is $800.

Answer:

$800

Step-by-step explanation:

Let the original price be x.

Final price=100%-75%

                  =25%

x-75%=200

x=200 x 100/75

x=8 x 100

x=800

Thank you!

I suppose you're supposed to convert 100111 from base 2 to base 10. We have

[tex]100111_2=2^5+2^2+2^1+2^0=32+4+2+1=39_{10}[/tex]

so the missing number is 39.

Answer:

£32 in total for the top and two trousers

Step-by-step explanation:

The price for a top In the "cloth for you" shop= £10

The price for a bermuda trouser In the "cloth for you" shop= £12

There is a 20% discount on tops

The price If I bought one top and would trouser will be

(10-(0.2*10)) for the top

2(12) for the trouser

Total= (10-(0.2*10))+ 2(12)

Total = 10-2+24

Total = £32

So I spent £32 in total for the top and two trousers

Answer:

The answer is option C

Step-by-step explanation:

x² - 7x + 10

To factor the expression rewrite - 7x as a difference

That's

x² - 5x - 2x + 10

Factor out x from the expression

x( x - 5) - 2x + 10

Factor - 2 from the expression

x(x - 5) - 2( x - 5)

Factor out x - 5 from the expression

The final answer is

Hope this helps you

Answer:

d. 27 cubic feet

Step-by-step explanation:

volume of cube = s^3 = B * s

volume of pyramid = (1/3) * B * h

The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.

volume of pyramid = 9 cu ft

volume of cube = 3 * 9 cu ft = 27 cu ft

Answer: d. 27 cubic feet

Answer:

27 ft^3 (Answer d)

Step-by-step explanation:

Here the volume of the pyramid is (1/3) the volume of the cube:

Letting s represent the length of one side of the base,

(1/3)(s)^2(s) = 9 ft^3, equivalent to  s^3 = 27.

Solving for s, we get s = 3 ft.

Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)

Answer: 0.0993

Step-by-step explanation:

Since the jar contains 18 red marbles and 38 blue marbles, the total marbles will be:

= 18 marbles + 38 marbles

= 56 marbles

When 2 marbles are pull out at random at the same time, the probability that both are red will be:

= (18/56) × (17/55)

= 0.3214 × 0.3091

= 0.0993

Answer:

x =  12      ( two points shots )

y =  7       ( three points shots )

Step-by-step explanation:

Let´s call  "x" two points shots,  and  "y" three points shots, then

x  +  y  =  19

2*x  +  3*y  =  45

We have to solve a two-equation system for x and y

y =  19  - x

2*x  +  3 * ( 19 - x ) = 45

2*x  +  57  -  3*x   =  45

- x   =  45 - 57

-x   =  - 12

x  = 12

And     y  =  19  -  12

y  = 7

Answer:

C = pi sqrt(x)

Step-by-step explanation:

The area of a square is x

A = s^2 where s is the side length

x = s^2

Take the square root of each side

sqrt(x) = s

This would be the diameter of the inscribed circle

The circumference of a circle is given by

C = pi d

C = pi sqrt(x)

Answer:

See below.

Step-by-step explanation:

Assign the variable n to be the sides of the square.

Since a square has four equal sides, the area of the square is n^2 or x.

Therefore:

[tex]n=\sqrt{x}[/tex]

The largest circle that can be inscribed in the square will have the largest possible diameter. The largest possible diameter will be straight across the center of the circle. So, the largest possible diameter will be the side length, n.

Therefore, the radius will be n/2.

The circumference of a circle is:

[tex]C=2\pi r[/tex]

Plug in n/2 for the radius:

[tex]C=2\pi (\frac{n}{2})\\ C=n\pi[/tex]

Now, substitute n for the square root of x:

[tex]C=\pi\sqrt{x}[/tex]

Answer:

A. y + 2= x

Step-by-step explanation:

Which equation is represented by the graph shown in the image?

A. y + 2= x

B. y + 1= x

C. y - 1= x

D. y - 2= x

Please show ALL work! <3

The graph shown has a slope of +1 and a y intercept of -2.

All given answer choices have a slope of +1, so that's not the problem.

We need one that has a y-intercept of -2, or the equation should be

y = x-2, or equivalently y+2 = x

which corresponds to answer choice A.

Answer:

D

Step-by-step explanation:

[tex]4(x^2+3)-2y\\\\=4((-6)^2+3)-2(\frac{-1}{2} )\\\\=4(36+3)+1\\\\=4(39)+1\\\\=156+1\\\\=157[/tex]

The value of the expression 4(x² + 3) - 2y is 157, when x = -6 and y = -1/2.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

4(x² + 3) - 2y

Substitute x = -6 and y = -1/2 to find the value of expression,

= 4 ((-6)² + 3) - 2(-1/2)

= 4 (36 + 3) + 1

= 4 x 39 + 1

= 156 + 1

= 157

The required value of the expression is 157.

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Answer:

D

Step-by-step explanation:

Let's first find the mean and median of each class.

Class 1:

The mean is simply all the numbers added up and then divided by the number of elements. There are 9 students in Class 1. Thus, we add all the ages up and then divide by 9. Thus:

[tex]\text{Class 1 Mean }= \frac{14+15+15+16+16+16+17+17+18}{9} \\=144/9=16[/tex]

The median is simply the middle number when the data sets are placed in order. The median of Class 1 is 16, the number in the middle.

Class 2:

Again, Class 2 has 9 students. Add up all the ages and then divide:

[tex]\text{Class 2 Mean }= \frac{13+14+15+16+16+17+18+18+19}{9}\\ =146/9\approx16.2222[/tex]

The median is the middle number of the data set. The median of Class 2 is 16.

Therefore, the mean of Class 2 is larger than the mean of Class 1. The medians of the two classes are equivalent.

Of the answer choices given, only D is correct.

Answer:

The mean of class II is larger and the median is the same

Step-by-step explanation:

Class I

14,15,15,16,16,16,17,17,18

The mean is

(14+15+15+16+16+16+17+17+18)/9

144/9 = 16

The median is the middle number

14,15,15,16,    16,    16,17,17,18

median = 16

Class II

13,14,15,16,16,17,18,18,19

The mean is

(13+14+15+16+16+17+18+18+19)/9

146/9 = 16.2repeating

The median is the middle number

13,14,15,16    ,16,       17,18,18,19

median = 16

Answer:

The probability is 2,010,580/13,378,456

Step-by-step explanation:

Here is a combination problem.

We want to 7 cards from a total of 52.

The number of ways to do this is 52C7 ways.

Also, we know there are 12 face cards in a standard deck of cards.

So we are selecting 3 face cards from this total of 12.

So also the number of cards which are not face cards are 52-12 = 40 cards

Out of all these 40, we shall be selecting exactly 4. The number of ways to do this 40C4

Thus, the required probability will be;

(40C4 * 12C3)/52C7 = (91,390 * 220)/133,784,560

= 20,105,800/133,784,560 = 2,010,580/13,378,456

Answer:

5443

Step-by-step explanation:

Order of Operations: BPEMDAS

Always left to right.

Step 1: Add 68 and 5042

68 + 5042 = 5110

Step 2: Add 5110 and 333

5110 + 333 = 5443

And we have our answer!

Answer:

I hope you are searching for this......

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day

Step-by-step explanation:

We are given that a website developer wished to analyze the clicks per day on their newly updated website.

The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.

Let [tex]\mu[/tex] = mean number of clicks per day.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day

Here, the null hypothesis states that the mean number of clicks per day is 200 clicks a day.

On the other hand, the alternate hypothesis states that the mean number of clicks per day is different than 200 clicks a day.

Hence, this is the correct null and alternative hypotheses.

Answer: Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Step-by-step explanation:

Let [tex]\mu[/tex] be the mean number of clicks per day.

Given, a website developer wished to analyze the clicks per day on their newly updated website.

The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.

i.e. he wants to check either [tex]\mu=200\text{ or }\mu\neq 200[/tex]

Since a null hypothesis is a hypothesis believes that there is no difference between the two variables whereas an alternative hypothesis believes that there is a statistically significant difference between two variables.

So,  Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Hence, the required null and alternative hypotheses.

Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Answer:

The sum is represented by the polynomial:

[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]

Step-by-step explanation:

Recall that polynomials are added by combining like terms. The only like terms in this addition are: 5 x and 8 x  which added render: 13 x. therefore, the addition of these polynomials renders;

[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]