Alex wants to sew a pillow in the shape below. How many square yards of fabric are needed to sew the pillow? Fabric is only sold in increments of ¼ yard.

Answer:

Option (D)

x = 5

Step-by-step explanation:

Since point E is in the mid of the segment DF,

Therefore, by the Segment addition postulate,

DF = DE + EF

Since DF = (8x - 3), DE = (x - 3) and EF = (6x + 5)

By substituting these values in the given postulate,

(8x - 3) = (x - 3) + (6x + 5)

8x - 3 = (x + 6x) + (5 - 3)

8x - 3 = 7x + 2

8x - 7x = 3 + 2

x = 5

Therefore, x = 5 will be the answer.

Answer:

x=6 and D

Step-by-step explanation:

Answer:

Total expected amount = $0.04375

Step-by-step explanation:

We need to calculate probability of getting heads on every combination of coin tosses

HHH = 1/8 = 3 heads

HHT = 1/8 = 2 heads

HTH = 1/8 = 2 heads

HTT = 1/8 = 1 head

THH = 1/8 = 2 heads

THT = 1/8 = 1 head

TTH = 1/8 = 1 head

TTT = 1/8 = 0 head

So the probability of 3 heads is 1/8 and the amount is (1/8)* 0.14 = $0.0175

Probability of 2 heads is 3/8 and the amount is (3/8) * 0.06 = $0.0225

Probability of 1 head is 3/8 and amount is (3/8) * 0.01 = $0.00375

Total expected amount = 0.00375 + 0.0225 + 0.0175

Total expected amount = $0.04375

Answer:

1/3

Step-by-step explanation:

there are twelve marbles total. there are 4 blue marbles.

4/12 = 1/3

Answer:

integer of course

Step-by-step explanation:

an integer can either be negative or positive.

Answer:

A

Step-by-step explanation:

Answer:

A. There is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.

D. Fail to reject H0.

Step-by-step explanation:

From the summary of the given test statistics.

The null and the alternative hypothesis are:

[tex]H_0:\mu_1=\mu_2 \\ \\ Ha:\mu_1 \neq \mu_2[/tex]

This test is also a two tailed test.

Similarly, the t value for the test statistics = 1.44

The p- value - 0.167

The level of significance ∝ = 0.05

The objective we are meant to achieve here is to determine which of the following from the given options are appropriate conclusions for this hypothesis test.

From what we have above:

Decision Rule: We fail to reject the null hypothesis since the p-value is greater than the level of significance at 0.05

CONCLUSION: Therefore, we can conclude that  there is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag as we fail to reject H0.

Answer:

Inequality: 3 + 1.2c

What you'd put on graph: 1 ≥ 13.50

Answer:

(1+y^2) /2y

Step-by-step explanation:

arithmetic mean is the average of x and y

(x+y)/2

Using the equation

xy = 1

and solving for x

x = 1/y

Replacing x in the first equation

(1/y + y) /2

Multiply by y/y

(1/y + y) /2 * y/y

(1/y + y)*y /2y

(1+y^2) /2y

Answer:

∠NMC  = 50°

Step-by-step explanation:

The interpretation of the information given in the question can be seen in the attached images below.

In ΔABC;

∠ A + ∠ B + ∠ C = 180°    (sum of angles in a triangle)

∠ A + 70°  + 50°  = 180°

∠ A = 180° - 70° - 50°

∠ A =  180° - 120°

∠ A =  60°

In ΔAMN ; the base angle are equal , let the base angles be x and y

So; x = y   (base angle of an equilateral  triangle)

Then;

x + x + 60° = 180°

2x +  60° = 180°

2x = 180° - 60°

2x = 120°

x = 120°/2

x = 60°

∴ x = 60° , y = 60°

In ΔBQC

∠a + ∠e + ∠b = 180°

50° + ∠e + 40° = 180°

∠e = 180° - 50° - 40°

∠e = 180° - 90°

∠e = 90°

At point Q , ∠e = ∠f = ∠g = ∠h = 90°  (angles at a point)

∠i  = 50° - 40° = 10°

In ΔNQC

∠f + ∠i   + ∠j = 180°

90° + 10° + ∠j = 180°

∠j  = 180° - 90°-10°

∠j  = 180° - 100°

∠j  = 80°

From  line AC , at point N , ∠y + ∠c + ∠j = 180°   (sum of angles on a straight line)

60° + ∠c + ∠80° = 180°

∠c  = 180° - 60°-80°

∠c  = 180° - 140°

∠c  = 40°

Recall that :

At point Q , ∠e = ∠f = ∠g = ∠h = 90°  (angles at a point)

Then In Δ NMC ;

∠d + ∠h + ∠c = 180°   (sum of angles in a triangle)

∠d + 90° + 40° = 180°

∠d  = 180° - 90° -40°

∠d  = 180° - 130°

∠d  = 50°

Therefore, ∠NMC = ∠d  = 50°

Answer:

[tex]\large \boxed{\mathrm{34.2}}[/tex]

Step-by-step explanation:

[tex]\sf B= arcsin (\frac{b \times sin(A)}{a} )[/tex]

[tex]\sf B= arcsin (\frac{7 \times sin(40\°)}{8} )[/tex]

[tex]\sf B = 0.59733 \ rad = 34.225\°[/tex]

Step-by-step explanation:

It is given that, a projectile is fired vertically upward from a height of 300  feet above the ground, with an initial velocity of 900 ft/s.

The general equation with which a projectile are modled by the function is given by :

[tex]h(t)=-16t^2+v_ot+y_o[/tex]

y₀ is the initial height above the ground

v₀ = initial velocity

So,

[tex]h(t)=-16t^2+900t+300[/tex]

This is the quadratic equation that models the projectile height in feet above the ground after t seconds.

Answer:

Option (2)

Step-by-step explanation:

1). If two lines have the same slope, lines are defined as parallel.

m₁ = m₂

2). If the multiplication of the slopes of two lines is (-1), lines will be perpendicular.

m₁ × m₂ = (-1)

Line 1 : It passes through two points (-2, 10) and (1, 1).

Slope of the line 1 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                              = [tex]\frac{1+2}{10-1}[/tex]

                              = [tex]\frac{3}{9}[/tex]

                         m₁ = [tex]\frac{1}{3}[/tex]

Line 2 : It passes through two points (-2, 8) and (2, -4).

Slope of the line 2 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                               = [tex]\frac{8+4}{-2-2}[/tex]

                               = [tex]-\frac{12}{4}[/tex]

                         m₂ = -3

Since, m₁ × m₂ = [tex]\frac{1}{3}\times (-3)[/tex]

                        = (-1)

Therefore, given lines are perpendicular to each other.

Option (2) is the correct option.

[tex]5(2x + 4) = 15\\10x+20=15\\10x=-5\\x=-\dfrac{5}{10}=-0,5[/tex]

Answer:

[tex]\huge\boxed{x=-0.5}[/tex]

Step-by-step explanation:

[tex]5(2x+4)=15\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup(2x+4)}{5\!\!\!\!\diagup}=\dfrac{15\!\!\!\!\!\diagup}{5\!\!\!\!\diagup}\\\\2x+4=3\qquad\text{subtract 4 from both sides}\\\\2x+4-4=3-4\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{-1}{2}\\\\\boxed{x=-0.5}[/tex]

Answer:

Step-by-step explanation:

Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.

Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229

Also, the ratio of the sample students with math score below grade level to sample population will be 163:452

On equating both ratios, we will have;

x:2229 =  163:452

[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]

Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804

Answer:

[tex]\{P^2: P\ E\ Z\ and\ 1\leq p\leq 10\}[/tex]

Step-by-step explanation:

Given

Range: = 1 to 100 (Inclusive)

Required

Determine the notation that represents the perfect square in the given range

Represent the range with P

P = 1 to 100

Such that the perfect squares will be P² and integers

In set notation, integers are represented with Z

The set notation becomes

[tex]\{P^2: P\ E\ Z\ and\ 1\leq p\leq 10\}[/tex]

The [tex]\leq[/tex] shows that 1 and 100 are inclusive of the set

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.

[tex]\text{Solve for x:}\\\\-3x+9-2x=-12-5x\\\\\text{Combine like terms}\\\\-5x+9=-12-5x\\\\\text{Add 5x to both sides}\\\\9=-12\\\\\text{Since that's not valid, there would be no solutions}\\\\\boxed{\text{No solutions}}[/tex]

Answer:

The probability that the assembly line will be shut down is 0.00617.

Step-by-step explanation:

We are given that a soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification.

Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration.

Let X = Number of bottles in the sample that are not within specification.

The above situation can be represented through binomial distribution;

[tex]P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r};x=0,1,2,3,.....[/tex]

where, n = number of trials (samples) taken = 12 bottles

             x = number of success  = 2 or more bottles

            p = probabilitiy of success which in our question is probability that  

                 bottles are not within specification, i.e. p = 0.01

So, X ~ Binom (n = 12, p = 0.01)

Now, the probability that the assembly line will be shut down is given by = P(X [tex]\geq[/tex] 2)

  P(X [tex]\geq[/tex] 2) = 1 - P(X = 0) - P(X = 1)

                 = [tex]1-\binom{12}{0} \times 0.01^{0}\times (1-0.01)^{12-0}-\binom{12}{1} \times 0.01^{1}\times (1-0.01)^{12-1}[/tex]

                 = [tex]1-(1 \times 1\times 0.99^{12})-(12 \times 0.01^{1}\times 0.99^{11})[/tex]

                 = 0.00617

Answer:

Step-by-step explanation:

Given

Garden: [tex]x^2+18x+81[/tex]

One Bag: [tex]x^2 - 81[/tex]

Requires

Determine the number of bags to cover the whole garden

This is calculated as thus;

[tex]Bags = \frac{x^2+18x+81}{x^2 - 81}[/tex]

Expand the numerator

[tex]Bags = \frac{x^2+9x+9x+81}{x^2 - 81}[/tex]

[tex]Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}[/tex]

[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 81}[/tex]

Express 81 as 9²

[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}[/tex]

Evaluate as difference of two squares

[tex]Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}[/tex]

[tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]

Hence, the number of bags is [tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]

Answer:

B is the correct answer.

Step-by-step explanation:

-2x+3y+z=-6

z=6

-2x+3y+6=-6

-2x+3y=-12

-2(3)+3(2)

-6+6=0 A is incorrect

-2(3)+3(-2)=-12

-6-6=-12

B is the correct answer.

I am not going to show C or D, because you have the right answer. Hope this helps you. Thank you.

Answer:

Step-by-step explanation: Let all unknown no be x

Five more than the square of a number

= [tex]5 + x^2[/tex]

Five more than twice a number ;

[tex]5+2x\\= 2x+5[/tex]

Five less than the product of 3 and a number ;

[tex]5- 3x\\= 3x-5[/tex]

Twice the sum of a number and 5 ;

[tex]2(x+5)\\[/tex]

The sum of twice a number and 5 ;

[tex]2x+5[/tex]

The product of the cube of a number and 5;

[tex]x^3 \times 5\\=5x^3[/tex]

The cube of the product of 5 and a number ;

[tex](5\times x)^3\\(5x)^3[/tex]

Answer:

D. [tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]

Step-by-step explanation:

Given

[tex]y = \frac{2}{5}x - 5[/tex]

Required

Determine its equivalent

From the list of given options, the correct answer is

[tex]x - \frac{5}{2}y = \frac{25}{2}[/tex]

This is shown as follows;

[tex]y = \frac{2}{5}x - 5[/tex]

Multiply both sides by [tex]\frac{5}{2}[/tex]

[tex]\frac{5}{2} * y = \frac{5}{2} * (\frac{2}{5}x - 5)[/tex]

Open Bracket

[tex]\frac{5}{2} * y = \frac{5}{2} * \frac{2}{5}x - \frac{5}{2} *5[/tex]

[tex]\frac{5}{2}y = x - \frac{25}{2}[/tex]

Subtract x from both sides

[tex]\frac{5}{2}y - x = x -x - \frac{25}{2}[/tex]

[tex]\frac{5}{2}y - x = - \frac{25}{2}[/tex]

Multiply both sides by -1

[tex]-1 * \frac{5}{2}y - x * -1 = - \frac{25}{2} * -1[/tex]

[tex]-\frac{5}{2}y + x = \frac{25}{2}[/tex]

Reorder

[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]

Hence, the correct option is D

[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]

Answer:

The 4th option

Step-by-step explanation:

Answer: 20 sq. units .

Step-by-step explanation:

Let A(0, -2), B(3,2), C(8,2), and D(5, -2) are the points for the parallelogram.

First we plot these points on coordinate plane, we get parallelogram ABCD.

By comparing the y-coordinate of B and C with A and D , we get

height = 2+2 = 4 units

Also by comparing the x coordinates of A and D, we get base = 5-0= 5 units  

Area of parallelogram = Base x height

= 5 x 4 = 20 sq. units

Hence, the area of a parallelogram ABCD is 20 sq. units .

Answer:

p(n) = -1/100 n  40

Step-by-step explanation:

Use the two points (n, p): (1000, 30) and (3000, 10).

Now we find the equation of the line that passes through these two points.

m = (10 - 30)/(3000 - 1000)

m = -20/2000

m = -1/100

p(n) = mn + b

30 = -1/100 * 1000 + b

30 = -10 + b

b = 40

The equation is:

p(n) = -1/100 n  40

Answer:

a

   The  null hypothesis is  [tex]H_o : \mu = 35 .1 \ million \ shares[/tex]

    The  alternative hypothesis  [tex]H_a : \mu \ne 35.1\ million \ shares[/tex]

b

 The   95% confidence interval is  [tex]27.475 < \mu < 37.925[/tex]

Step-by-step explanation:

From the question the we are told that

      The  population mean is  [tex]\mu = 35.1 \ million \ shares[/tex]

      The  sample size is  n = 30

       The  sample mean is  [tex]\= x = 32.7 \ million\ shares[/tex]

       The standard deviation is  [tex]\sigma = 14.6 \ million\ shares[/tex]

Given that the confidence level is  [tex]95\%[/tex] then the level of significance is mathematically represented as

                  [tex]\alpha = 100-95[/tex]

                  [tex]\alpha = 5\%[/tex]

=>               [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table

    The value is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

                 [tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{\sqrt{n} }[/tex]

substituting values

                [tex]E = 1.96 * \frac{ 14.6 }{\sqrt{30} }[/tex]

                [tex]E = 5.225[/tex]

The 95% confidence interval confidence interval is mathematically represented as

              [tex]\= x -E < \mu < \= x +E[/tex]

substituting values

               [tex]32.7 - 5.225 < \mu < 32.7 + 5.225[/tex]

                [tex]27.475 < \mu < 37.925[/tex]

Answer:

[tex]71,100[/tex]

Step-by-step explanation:

If you are trying to find a number that is written in word form, we can just use place values to find what goes where.

A number is broken down into this:

Ten thousands, thousands, hundreds, tens, ones.

If they have 7 ten thousands, the first digit will be a 7.

If they have 1 thousand, the second digit will be a 1.

If they have 1 hundred, the third digit will be a 1.

Since nothing is stated about tens, we assume it's value is 0.

And since there are no ones, it's value is 0.

So:

71,100.

Hope this helped!

Answer:

x=18

Step-by-step explanation:

x/6 - 7 = -4

x/6 = 3

(x/ 6) * 6 = 3*6

x = 18

Answer:

2hrs 24mins

Step-by-step explanation:

Very simple the time they will meet again at the point will be the LCM of their various time taken to complete a cycle.

Ans LCM(24, 36, 48) = 144 mins

= 2hrs 24mins

Answer:

The answer is 2 hours and 24 minutes

Step-by-step explanation:

Hope you get this right:)

Answer:

-15

Step-by-step explanation:

If it fell 3 deg every hour for 5 hours so the equation is 3*5 plus a - sign because it dropped degrees

Answer:

17,720 ft

Step-by-step explanation:

5.4 km * (1 mile)/(1.609 km) * (5280 ft)/(1 mile) = 17,720 ft