The triangles are similar. Write a similarity statement for the triangles.

Answer:

x = 6

Step-by-step explanation:

I will use some symbols, please refer to the image I attach to understand my answer.

Since BC = 2 using Thales theorem we get that

3/x = 2/4      then 3/x = 1/2    and 6 = x

Answer:

width of the garden is 50 ft and the length is 70 ft

Step-by-step explanation:

Solution:-

- We will denote the width and and the length of the rectangular garden as:

   Width: x

   Length: x + 20

- We are given the area ( A ) of the garden is 3500 ft^2. We are to determine for what dimensions is the area A = 3500 ft^2.

- Recall that the area ( A ) of a rectangle is the product of length and width as follows:

                      A = Length * width

                      A = x*( x + 20 )

                      3500 = x^2 + 20x

                      x^2 + 20x - 3500 = 0

- Use the quadratic formula to determine the value of ( x ):

                     [tex]x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-20 +/- \sqrt{20^2 - 4*-3500} }{2}\\\\x = \frac{-20 +/- 120 }{2} = -10 +/- 60\\\\x = -70 , 50[/tex]

- Ignore the negative value of ( - 70 ft ). Physical impractical to have a negative value. Hence, the width of the garden is 50 ft and the length is 70 ft

Answer:

Step-by-step explanation:

a. To identify the alternative hypothesis, we have to examine the claim

The claim is that the mean nickel diameter drawn by children in the low income group is greater than 21.21 mm

Thus, alternative hypothesis is μ > 21.21

b. The test statistics is

z score = x - u /(sd/√n)

Where x (sample mean) is 23.375, u is pop. mean is 21.21, sd is 5.29 and n (sample size) is 40

z = 23.375 - 21.21 /(5.29/√40)

z = 2.165 / (5.29/6.3246)

z = 2.165/0.8364

z = 2.588

c. The critical value is

Alpha for this case study is 0.01. Then the critical probability is 1 - (alpha/2) =

1 - (0.01/2) = 1 - 0.005 = 0.995

To express the critical value as a z score, find the z score corresponding to the critical probability using the z table. Which is 0.8389.

Answer:

3200ft^2

Step-by-step explanation:

1 inch = 4ft

so 20 inches = 80ft

and 10 inches = 40ft

Area = 80ft*40ft

Area = 3200ft^2

Answer:

(Y-3)= -1/3(x-7)

Or

(Y-4)= -1/3(x-4)

Steb by step explanation:

The condition for the line is (7,3) and (4,4).

Point slope form of equation is in this format below.

(Y-y1)= m(x-x1)

We have the given parameters in the above format except the m

M = gradient

Gradient= (y2-y1)/(x2-x1)

Gradient=(4-3)/(4-7)

Gradient= 1/-3

Gradient= -1/3

So

(Y-y1)= m(x-x1)

(Y-3)= -1/3(x-7)

Or

(Y-4)= -1/3(x-4)

Answer: a) 0.8708, b) 5714, c) 0.000, d) 0.3830

Step-by-step explanation:

(a)

To find P(Z>-1.13):

Since Z is negative, it lies on left hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.3708

So,

P(Z>-1.13) = 0.5 + 0.3708 = 0.8708

(b)

To find P(Z<0.18):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.0714

So,

P(Z<0.18) = 0.5 + 0.0714 = 0.5714

(c)

To find P(Z>8):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.5 nearly

So,

P(Z>8) = 0.5 - 0.5 nearly = 0.0000  

(d)

To find P(| Z | < 0.5)

that is

To find P(-0.5 < Z < 0.5):

Case 1: For Z from - 0.5 to mid value:

Table of Area Under the Standard Normal Curve gives area = 0.1915

Case 2: For Z from mid value to 0.5:

Table of Area Under the Standard Normal Curve gives area = 0.1915

So,

P(| Z | < 0.5) = 2 * 0.1915 = 0.3830

The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.

(a) The value of [tex]P(z>-1.13)=0.8708[/tex].

(b) The value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c) The value of [tex]P(Z > 8) = 0.0000[/tex].

(d) The value of [tex]P(| Z | < 0.5) =0.3830[/tex].

Given:

The given condition is [tex]Z\sim N(\mu= 0,\sigma = 1).[/tex]

(a)

Find the value for [tex]P(Z > -1.13)[/tex].

Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.3708[/tex].

Now,

[tex]P(Z > -1.13)=0.5 + 0.3708 = 0.8708[/tex]

Thus, the value of [tex]P(z>-1.13)=0.8708[/tex].

(b)

Find the value for [tex]P(Z < 0.18)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.0714[/tex].

Now,

[tex]P(Z <0.18)=0.5 + 0.0714 = 0.5714[/tex]

Thus, the value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c)

Find the value for [tex]P(Z >8)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area \approx 0.5[/tex].

Now,

[tex]P(Z >8)\approx0.5 - 0.5 = 0.0000[/tex]

Thus, the value of [tex]P(Z > 8) = 0.0000[/tex].

(d)

Find the value for [tex]P(|Z| <0.05)[/tex].

Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Consider the positive  value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Now,

[tex]P(|Z| <0.5)=2\times 0.1915 = 0.3830[/tex]

Thus, the value of [tex]P(| Z | < 0.5) =0.3830[/tex].

Learn more about z-table here:

https://brainly.com/question/16051105

Answer:

12/13

Step-by-step explanation:

First we must calculate the hypotenus using the pythagoran theorem

Now let's calculate sin0

So the exact value is 12/13

Answer:

C.) 12/13

Step-by-step explanation:

In a right angle triangle MN = 12, ON = 5 and; angle N = 90°

Now,

For hypotenuse we will use Pythagorean Theorem

(MO)² = (MN)² + (ON)²

(MO)² = (12)² + (5)²

(MO)² = 144 + 25

(MO)² = 169

MO = √169

MO = 13

now,

Sin O = opp÷hyp = 12÷13

Answer:

83.0

Step-by-step explanation:

We have all three sides and the only thing we're missing is the X angle. And that's okay!

All you have to do is plug in the numbers into each variable. In this case if you are going to solve for X, you should use this equation.

[tex]x^2=y^2+z^2-2yzcosX[/tex]

x = 17ft

y = 8ft

x = 16fi

Then you can algebraically solve for cosX, and then use the inverse of cosx to get the angle.

Answer:

option 3

Step-by-step explanation:

4x+8<-16

x<-6

4x+8_>-16

x_>-1

(it's more and equal .so the circle has to be shaded and move to the right of -1)

Answer:C

Step-by-step explanation:

Answer:

The center is (1,4)

Step-by-step explanation:

The coordinates of the center of an ellipse are the coordinates that are in the middle of the two focus.

Then if we have a focus on [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], we can say that the coordinates for x and y can be calculated as:

[tex]x=\frac{x_1+x_2}{2}\\ y=\frac{y_1+y_2}{2}[/tex]

So, replacing [tex](x_1,y_1)[/tex] by (-4,4) and [tex](x_2,y_2)[/tex] by (6,4), we get that the center is:

[tex]x=\frac{-4+6}{2}=1\\ y=\frac{4+4}{2}=4[/tex]

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            Hi my lil bunny!

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Let's solve your equation step-by-step.

[tex]\frac{1}{3} (x+1)+2x=2[/tex]

Step 1: Simplify both sides of the equation.

[tex]\frac{1}{3} (x+1)+2x=2[/tex]

[tex](\frac{1}{3}) (x) + (\frac{1}{3} ) (1) + 2x = 2[/tex] (Distribute)

[tex]\frac{1}{3} x + \frac{1}{3} + 2x = 2[/tex]

[tex]( \frac{1}{3} x + 2x ) + (\frac{1}{3}) = 2[/tex] (Combine Like Terms)

[tex]\frac {7}{3} x + \frac{1}{3} = 2\\\frac{7}{3} x + \frac{1}{3} = 2[/tex]

Step 2: Subtract 1/3 from both sides.

[tex]\frac{7}{3} x + \frac{1}{3} - \frac{1}{3} = 2 - \frac{1}{3} \\\\\frac{7}{3} x = \frac{5}{3}[/tex]

Step 3: Multiply both sides by 3/7.

[tex]( \frac{3}{7} ) * (\frac{7}{3}x) = ( \frac{3}{7}) * \frac{5}{3} \\\\x = \frac{5}{7}[/tex]

So the answer is : [tex]x = \frac{5}{7}[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

(a) $7/ticket

(b) 3 cats/dog

(c) 10 ft/sec

(d) 16 cups/gal

Step-by-step explanation:

(a) $35 for 5 tickets

$35/(5 tickets) = $7/ticket

(b) 21 cats and 7 dogs

21 cats/(7 dogs) = 3 cats/dog

(c) 40 ft in 4 seconds

40 ft/(4 sec) = 10 ft/sec

(d) 48 cups for 3 gallons

48 cups/(3 gal) = 16 cups/gal

Answer:

Step-by-step explanation:

Given that:

the standardized test scores of the students in a school are normally distributed with:

mean = 85 points

standard deviation = 3 points

Using the empirical rule:

=85 - (3 × 3)

= 85 - 9

= 76

The given value of 76 points is 3 standard deviations below mean

Therefore;

the percent score between the given value of 76 points and the  mean 85 points is:

99.7/2 = 49.85%   ( since 99.7 data value lies within 3 standard deviation)

Also ; the percent of value above the mean score = 50%

Therefore, the probability that a student's score is greater than 76 points is

= (49.85 + 50 )%

 = 99.85%

Answer:

mean=85

sd=3

85-3*3=76

its between 76 and 85=99.7/2=49.85%

50% mean above.

49.85+50=99.85%

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Let's break this down step by step:

"2 digit positive odd integers greater than 50"

So we start at 50

Don't exceed 99 since 2-digit limit

Any 2-digit integer greater than 50 will be positive (So that's a redundant statement)

Well...we know that from 50-99, is 50 integers counting by ones.

We know that half will be even and half will be odd.

With this we can say 50/2 == 25

Hence, there are 25 2 digit positive odd integers greater than 50.

Cheers.

Answer:

1/36

Step-by-step explanation:

the fair die has 6 equal parts which means its the total

the probability of rolling a 6 is 1/6

the probability of rolling another 6 is 1/6

so u multiply 1/6 times 1/6 which is 1/36

hope this helps

Hey there

Answer:

a

   The Null hypothesis is  [tex]H_o : p = 0.01[/tex]

   The defect did not exceed 0.01

b

   The  95%  confidence interval is   [tex]0.004801 < p < 0.020199[/tex]

   Yes the CI agrees with the result in a  because the value 0.01 fall within the CI

Step-by-step explanation:

From the question we are told that

     The sample size is  n = 800

      The number of defective calculators is  k =  10

       The population is  [tex]p = 0.01[/tex]

The Null hypothesis is  [tex]H_o : p = 0.01[/tex]

The Alternative hypothesis is  [tex]H_a : P> 0.01[/tex]

Generally the proportion of defective calculators is mathematically represented as

         [tex]\r p = \frac{k}{n}[/tex]

substituting values

          [tex]\r p = \frac{10}{800}[/tex]

          [tex]\r p = 0.0125[/tex]

Next is to obtain the critical value of  [tex]\alpha[/tex] from the z-table.The  value is  

          [tex]Z_{\alpha } = 1.645[/tex]

Now the test statistics is mathematically evaluated as

        [tex]t = \frac{\r p - p }{ \sqrt{ \frac{p (1- p )}{n} } }[/tex]

substituting values

          [tex]t = \frac{ 0.0125 - 0.01 }{ \sqrt{ \frac{0.01 (1- 0.01 )}{800} } }[/tex]

           [tex]t = 0.71067[/tex]

Now comparing the values of  t to the value of [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis

Generally the margin of error is mathematically represented as  

       [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1-\r p )}{n} }[/tex]

where  [tex]Z_{\frac{\alpha }{2} }[/tex] is the critical value of  [tex]\frac{\alpha }{2}[/tex] which is obtained from the z-table.The  value is

              [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 1.96[/tex]

The reason we are obtaining critical value of    [tex]\frac{\alpha }{2}[/tex]  instead of    [tex]\alpha[/tex] is because    [tex]\alpha[/tex]

represents the area under the normal curve where the confidence level interval (   [tex]1- \alpha[/tex] ) did not cover which include both the left and right tail while  

 [tex]\frac{\alpha }{2}[/tex]  is just the area of one tail which what we required to calculate the margin of error .

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

So

      [tex]E = 1.96 * \sqrt{\frac{ 0.0125 (1-0.0125 )}{800} }[/tex]

     [tex]E = 0.007699[/tex]

The  95%  confidence interval is mathematically represented as

       [tex]\r p - E < p < \r p - E[/tex]

substituting values

      [tex]0.0125 - 0.007699 < p < 0.0125 + 0.007699[/tex]

      [tex]0.004801 < p < 0.020199[/tex]

Now given the p = 0.01 is within this interval then the CI  agrees with answer gotten in a

Answer:

1

Step-by-step explanation:

[tex]\frac{kyz}{1}*\frac{1}{kyz} =\frac{kyz}{kyz}=1[/tex]

Step-by-step explanation:

(ax + b)² = a²x² + 2abx + b²

In this case, a = 1, so:

14 = 2b

b = 7

(x + 7)² = x² + 14x + 49

Answer: The length of the line B'C" is 1 unit.

Step-by-step explanation:

Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.

If A (2,2), B= (4,3) and C=(6,3).

Distance between (a,b) and (c,d): [tex]D=\sqrt{(d-b)^2+(c-b)^2}[/tex]

Then, BC [tex]=\sqrt{(3-3)^2+(6-4)^2}[/tex]

[tex]\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}[/tex]

Length of image = scale factor x length in original figure

B'C' = 0.5 × BC

= 0.5 × 2

= 1 unit

Hence, the length of the line B'C" is 1 unit.

Answer:

y = 3/8x

or

3/8 cups of sugar for every 1/2 batch of muffins

Step-by-step explanation:

Since we are only making 1/2 of the full batch of muffins, we only need to use 1/2 the cups of sugar:

[tex]\frac{3}{4} (\frac{1}{2} )= \frac{3}{8}[/tex] cups of sugar.

Answer:

[tex]\frac{x}{2} = \frac{3y}{8}[/tex]

Step-by-step explanation:

Let the batch be x and the amount of sugar be y

Condition:

x = [tex]\frac{3}{4} y[/tex]

Multiplying both sides by 1/2

[tex]\frac{1}{2} x = \frac{3}{4}y * \frac{1}{2}[/tex]

[tex]\frac{x}{2} = \frac{3y*1}{4*2}[/tex]

[tex]\frac{x}{2} = \frac{3y}{8}[/tex]

So, For 1/2 batch of muffins, Farid need 3/8 cups of sugar.

Answer:

1/2

Step-by-step explanation:

The probability of taking a yellow ball can be found by dividing the number of yellow balls over the total number of balls.

P(yellow ball)= yellow balls / total balls

There are 10 yellow balls. There are a total of 20 balls. There are 20 because there are 10 yellow, 5 orange, and 5 green. When 10, 5, and 5 are added, the result is 20.

yellow balls = 10

total balls= 20

P(yellow ball)= yellow balls / total balls

P(yellow ball)= 10/20

The fraction 10/20 can be simplified. Both the numerator( top number) and denominator (bottom number) can be evenly divided by 10.

P(yellow ball)= (10/10) / (20/10)

P(yellow ball)= 1/(20/10)

P(yellow ball)= 1/2

The probability of taking a yellow ball is 1/2.

Answer:

x =2

Step-by-step explanation:

3 = 1/2x + 1/2x + 1/2x

Combine like terms

3 = 3/2 x

Multiply each side by 2/3 to isolate x

3 * 2/3 = 2/3 * 3/2 x

2 =x

Answer: C. Interest will be charged

Step-by-step explanation:

Answer:

Step-by-step explanation:

Interest will be charged is your answer!

Answer:

7 is the answer

Step-by-step explanation:

if we put 1/4 or 2 then the statement will wrong so 7 is the right answer

Answer:

A

Step-by-step explanation:

If 4A (7) is greater than 10, then 4x7=28. 28 is greater than 10.

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

Hope this helps you...

Answer:

(B)[tex]4\sqrt{37}[/tex]

Step-by-step explanation:

First, we determine the height of the triangle which we label as y.

Using Pythagoras Theorem.

[tex]25^2=7^2+y^2\\y^2=25^2-7^2\\y^2=576\\y=\sqrt{576}\\y=24[/tex]

In the smaller right triangle with hypotenuse, x

Base = 7-3 =4 Units

Height, y= 24 Units

Therefore, applying Pythagoras Theorem.:

[tex]x^2=24^2+4^2\\x^2=592\\x=\sqrt{592}\\ x=4\sqrt{37}[/tex]

Answer:

C. It is one-half the area of a square of side length 4 units.

Step-by-step explanation:

Hey there!

Well if a square has side lengths of 4 units,

the area would be 16 because of l*w.

Now the formula for the area of a triangle is,

b*h/2

b = 4

h = 4

4*4=16

16 ÷ 2 = 8

So the area of a square is 16 units^2 whereas the area of a triangle with the same dimensions is 8 units^2,

meaning the area of a triangle is one-half the area of a square.

Hope this helps :)

Answer:

The numbers should be less than 16 . The numbers can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ............15

Step-by-step explanation:

Eight less than four times a number is less than 56 . The expression can be written below

let

the number  = a

4a - 8 < 56

add 8 to both sides

4a - 8 + 8 < 56 + 8

4a < 64

divide both sides by 4

a < 64/4

a < 16

The numbers should be less than 16 . The numbers can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ............15

Answer:

19)

[tex]\frac{1}{2}*\frac{1}{4}*\frac{1}{8}*\frac{1}{16} = 2^n[/tex]

Notice that in the left side, all the numbers are powers of 2.

2 = 2^1

4 = 2^2

8 = 2^3

16 = 2^4

remember that:

(a^x)*(a^y) = a^(x+y)

then the denominator in the left is:

(2*4*8*16) = 2*(2^2)*(2^3)*(2^4) = 2^(1 + 2 + 3+ 4) = 2^8

Then we have:

[tex]\frac{1}{2}*\frac{1}{4}*\frac{1}{8}*\frac{1}{16} = \frac{1}{2^8} = 2^n[/tex]

[tex]1 = 2^8*2^n = 2^{8 + n}[/tex]

then 8 + n = 0

then n = -8.

18)

here we have:

x = (x/9) + (x/6) + (x/2) + 4 + (x/12) + 2

now in the left side we can use the common factor x and write it as:

x = x*( 1/12 + 1/9 + 1/6 + 1/2) + 6

x = x*(0.861) + 6

x - x*(0.861) = 6

x*(1 - 0.861) = 6

x = 6/(1 - 0.861) = 43.2

Work Shown:

A = P*(1+r/n)^(n*t) .... compound interest formula

A = 200(1+0.07/1)^(1*5) .... plug in given info

A = 200*(1.07)^5

A = 200*1.4025517307

A = 280.51034614

A = 280.51