D. _116 in. 14| Find the value of x to make the equation true. n2 = (n) 19 Which number V1272 A. 5 A. x= -1 B. X=1 x = 2 D. = x= 2 C 12 D. 62 Illuminate ItembankTM C.

Answer:

short story has 32 pgs

novel has 416 pgs

Step-by-step explanation:

a novel (N) has 13 times as many pages as a short story (x) so, N = 13X

total pages is the equation N + x = 448

plug the equation for N into this

13x + x = 448, combine like terms

14x = 448, divide both sides by 14

x = 32. so now we know that the short story has 32 pages. subtract that from 448. and the novel has 416 pages.

There are 32 pages in the short story and 416 pages in the novel.

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

Let x be the number of pages in the short story.

We know that the novel has 13 times as many pages as the short story, so the number of pages in the novel is 13x.

The combined number of pages in the books is the sum of the number of pages in the short story and the number of pages in the novel, which is x + 13x = 14x = 448 pages.

So the number of pages in the short story is x = 32 pages.

And the number of pages in the novel is 13x = 13 × 32 = 416 pages.

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The answers are 4. a) 15.7 cm, b) 26.25 m, 5. a) 128.74 cm, b) 40.82 mm, c) 45 cm and 6. 777.28 cm

Given are the circles and the circular items we need to find their circumference,

Circumference of a circle = 2π × radius = Diameter × π

4. a) Circumference = 5 × 3.14 = 15.7 cm

b) Circumference = 8.36 × 3.14 = 26.25 m

5. a) Circumference = 41 × 3.14 = 128.74 cm

b) Circumference = 13 × 3.14 = 40.82 mm

c) Circumference = 14.3 × 3.14 = 45 cm

6.

The perimeter of the cloth = circumference of the circular ends plus length in the middle,

= 76 × 2 × 3.14 + 150 × 2

= 477.28 + 300

= 777.28 cm

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Answer:

See below

Step-by-step explanation:

x is the smaller number

x + 2     is the other (larger) number

4 (x+2)  + x^2   = 16

4x + 8 + x^2

x^2 + 4x - 8 = 0

x = 1.4641     via Quadratic Formula   ( the positive value)

  the other number is   3.4641

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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Answer:

Step-by-step explanation:

slope intercept: y = mx + b

where m is the slope and b is the y-intercept

Equation: y = -3x + 4

Since y-intercept is given, then we have the first point of the line as (0,4)

Let's find the value of x when y is 0

y = -3x + 4

0 = -3x + 4

3x = 4

x = 4/3

(4/3,0) ---second point

Since there are two points/coordinates already then we can now plot/graph.

The coordinates of the image after the given rotation transformation are;

A'(-1, -2)

B'(-9, -2)

C'(-6, -6)

D'(-6, -7)

A rotation is defined as a type of transformation which is a turn. This means it involves the figure being turned clockwise or counterclockwise on the coordinate plane.

Now, In rotation, the size and shape of the figure remains exactly the same.

We are given a triangle and the coordinates from the image are;

A(1, 2)

B(9, 2)

C(6, 6)

D(6, 7)

The formula we use to rotate a two-dimensional shape 180° about the origin is (x,y) → (-x,-y).

Thus, our new coordinates are;

A'(-1, -2)

B'(-9, -2)

C'(-6, -6)

D'(-6, -7)

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Answer:

94 more students should be included in the sample.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.99}{2} = 0.005\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.005 = 0.995\), so \(z = 2.575\)

Now, find the margin of error M as such

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

How many students we need to sample to be 99% sure that the sample mean x is within 1 semester hour of the population mean?

We need to survey n students.

n is found when M = 1.

We have that \(\sigma = 4.7\)

So

\(M = z*\frac{\sigma}{\sqrt{n}}\)

\(1 = 2.575*\frac{4.7}{\sqrt{n}}\)

\(\sqrt{n} = 2.575*4.7\)

\((\sqrt{n})^{2} = (2.575*4.7)^{2}\)

\(n = 146.47\)

Rounding up

147 students need to be surveyed.

How many more students should be included...?

53 have already been surveyed

147 - 53 = 94

94 more students should be included in the sample.

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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The value of the angle x is 30 degrees

To determine the value of the variable x, we need to know the triangle sum theorem.

The triangle sum theorem is a theorem in mathematics stating that the sum total of the interior angles in a triangle is equivalent to 180 degrees.

We should also note that angle at right angle is 90 degrees

Then, we have the angles written as;

90 degrees

2x degrees

x degrees

Equate the angles , we have;

2x + x + 90 = 180

collect the like terms, we have;

2x + x = 180 - 90

add or subtract the like terms, we have;

3x = 90

divide by the coefficient

x = 30

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Answer:

Each person would have to get 8.3 oz of the drink.

Step-by-step explanation:

100/12=8.3

(Sorry if I misunderstood your question)

Answer:

a

Step-by-step explanation:

Answer:

la respuesta que buscas es bastante simple pero no lo sé

Step-by-step explanation:

Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

Answer:

a) 4x to x is 75% decrease

b)0.25m

We want to find the percentage increase or decrease of each of the following;

Applying the formula;

a) 4x to x

b) 0.25m to 0.5m

Answer:

x1 = √(509) /100 + 3/10

x2  = -√(509) /100 + 3/10

Step-by-step explanation:

We do completing the square as follows:

1. Put all terms with variable on one side and the constants on the other side.

5x^2 - 3x = 25

2. Factor out the coefficient of the x^2 term.

5(x^2 - 3x/5) = 25

3. Inside the parentheses, we add a number that would complete the square and also add this to the other side of the equation. In this case we add 9/100 and on the other  side we add 9/20.

5(x^2 - 3x/5 + 9/100) = 25 + 9/20

4. We simplify as follows:

5(x^2 - 3x/5 + 9/100) = 25 + 9/20

5(x - 3/10)^2 = 509/20

(x - 3/10)^2 = 509/100

x1 = √(509) /100 + 3/10

x2  = -√(509) /100 + 3/10

The average number of hours that adults spend working each day is 8 hours and Ryan is correct because he got the average of 8 right.

We know that,

The sample mean is a statistic that is computed by taking the arithmetic mean of the values of a variable in a sample. If the sample is taken from probability distributions with a shared expected value, the sample mean is an estimator of that value.

The mean is gotten from the formula;

x' = ∑x/n

Number of hours of work per day are; 6, 7, 8, 9 and 10

Thus; sum up all of it

∑x = 6 + 7 + 8 + 9 + 10

∑x = 40

Mean is; x' = 40/5

x' = 8

Since Ryan concluded that the average is 8 hours,

Therefore,

We can say that Ryan is correct.

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Jordan spend 25 minutes writing each dayNoHow much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:D + W = 75W + 25 = DSo, we haveW + W + 25 = 75EvaluateW = 25This means that Jordan spends 25 minutes on writing is it possible?Based on the answer in (a), the truth statement is No

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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Answer:

D

Step-by-step explanation:

the equation for Josh is 500 + 40x while the equation for Vanessa is only 60x

if josh's account balance is greater than it would be josh > vanessa or vanessa < josh

Answer:

a

The  null hypothesis is \(H_o : \ \sigma^2 = 1.9\)

The alternative hypothesis is  \(H_a : \ \sigma^2 \ne 1.9\)  

b

 \(X^2 = 13.74\)

c

The decision rule is  

Reject the null hypothesis

d

The conclusion is  

There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.

Step-by-step explanation:

From the question we are are told that

   The variance is \(\sigma ^2 = 1.9\)

    The sample size is  n =  30  

    The  sample variance  is  \(s^2 = 0.9\)

    The level of significance is  \(\alpha = 0.05\)

The  null hypothesis is \(H_o : \ \sigma^2 = 1.9\)

The alternative hypothesis is  \(H_a : \ \sigma^2 \ne 1.9\)  

Generally the test statistics  is mathematically represented as

          \(X^2 = \frac{ (n- 1 ) * s^2 }{ \sigma^2 }\)

=>       \(X^2 = \frac{ (30 - 1 ) * 0.9 }{1.9 }\)

=>       \(X^2 = 13.74\)

Generally  from the degree of freedom is mathematically represented as

         \(df = n- 1\)

=>      \(df = 30 - 1\)

=>      \(df = 29\)

Generally from the chi distribution table the critical value of  \(\frac{\alpha}{2} \ and \ 1 - \frac{ \alpha }{2}\) at a degree of freedom  of  \(df = 29\) is  

       \(X^2 _{ \frac{\alpha }{2} , df } = X^2 _{ \frac{0.05 }{2} , 29 } = 45.7\)

=>     \(X^2 _{ 1 - \frac{\alpha }{2} , df } = X^2 _{1 - \frac{0.05 }{2} , 29 } = 16.0 5\)

Gnerally from the values obtained we see that

         \(X^2 < X^2 _{ 1 - \frac{\alpha }{2} , df }\) hence

The decision rule is  

Reject the null hypothesis

The conclusion is  

There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.

Answer:

Area of \(\triangle\)ACD = 4 \(ft^2\)

Area of \(\triangle\)ABC = 16 \(ft^2\)

Step-by-step explanation:

Given that:

D is a point on AB.

and ABC is a triangle.

AD:DB = 1 : 3

Area of \(\triangle\)CDB = 12 \(ft^2\)

Kindly refer to the attached image as per the given dimensions and values.

To find:

Area of \(\triangle\)ACD and Area of \(\triangle\)ABC = ?

Solution:

Formula for area of a triangle = \(\frac{1}{2}\times Base \times Height\)

The altitudes of triangles \(\triangle\)CDB and \(\triangle\)ACD are equal in dimensions.

Therefore the area of triangles \(\triangle\)CDB and \(\triangle\)ACD will be equal to the ratio of their bases.

Area of \(\triangle\)ACD : Area of \(\triangle\)CDB = AD: DB = 1 : 3

\(\Rightarrow\) Area of \(\triangle\)ACD = \(\frac{12}{3} = \bold{4 ft^2}\)

Area of \(\triangle\)ABC = Area of \(\triangle\)ACD + Area of \(\triangle\)CDB = 12 + 4 = 16 \(ft^2\)

Therefore, the answer is:

Area of \(\triangle\)ACD = 4 \(ft^2\)

Area of \(\triangle\)ABC = 16 \(ft^2\)

Answer:

20 and 35 because it says that she wrote a check.

Step-by-step explanation:

The exact value of sin(5π/12) is (√6 + √2)/4

From the question, we have the following parameters that can be used in our computation:

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

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Answer: No.

Step-by-step explanation: Unless the tenth place is a 0, a product of a 2 numbers with 1 decimal place cannot have a product for a whole number, even if you went on forever.

:)

Answer:

Step-by-step explanation:

P=2(a+b)

2(26+25)

=102 ans

Answer:

102 cm

Step-by-step explanation:

P=2(a+b)

P = 2(26+25)

= 2 * 51

= 102

The time at which the theatre does not have any customers is; Choice A: 11:00 PM

From the task content;

Hence, when C(x) = 0, the theater has no customers.

Divide through by x;

x = 11.

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Answer:A

Step-by-step explanation:

i did the test

Answer:

n=5

Step-by-step explanation:

Answer:

n=21

Step-by-step explanation:

Answer:

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

As per given drawing PQ is the segment bisector of XY.

The point W is the midpoint of XY. As per property of midpoint, XW and WY have equal length.

XW = 13 units, hence: