Question 12
Write an equation of a line that passes through (8,5) and (11, 14).

It would take the test administrator 48 seconds to allow for the performance of the task

So, if we want 97.5 percent, we must look it up in our z table. So I need to find the z score that is closest to.975, which is 1.96.

The 97.5th percentile point of the standard normal distribution is a quantity often used in probability and statistics for statistical computations. This figure is around 1.96, which means that 95% of the area under a normal curve is within 1.96 standard deviations of the mean.

As a result, the z score for the 97.5th percentile would be multiplied by the class standard deviation. As a result, we obtain;

1.96*6 = 11.76

Then, this new time gotten would be added to the first mean of the class,

As a result, we have 36+11.76 = 47.76 which is approximately 48

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Answer:

$91.5

Step-by-step explanation:

muffins: 210 carrot sticks:120

T= 0.35x + 0.15y (replace x as no. of muffins & y as no. of carrot sticks)

T= (0.35×210) + (0.15×120)

T= 73.5 + 18

T= 91.5

The transformation of the given function g(x) = ¹/₂|x + 4| - 3 using the format h(x) = a|bx + c| + d, gives;

a = ¹/₂

b = -1

c = 6

d = 3

We are given the function;

g(x) = ¹/₂|x + 4| - 3

Now, we are told that the function is first translated by 6 units upwards, and so this means a transformation of;

g(x) + 6 = ¹/₂|x + 4| - 3 + 6

g'(x) = ¹/₂|x + 4| + 3

Now, we are told that it now undergoes a transformation of 2 units to the right, this gives;

g"(x) =  ¹/₂|x + 4 + 2| + 3

g"(x) = ¹/₂|x + 6| + 3

Finally, after undergoing a transformation of reflection in the y-axis, we have; h(x) = ¹/₂|-x + 6| + 3

For the format of;

h(x) = a|bx + c| + d, it means that we have;

a = ¹/₂

b = -1

c = 6

d = 3

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Triangles ABC and DEF are mathematically similar. The area of triangles ABC is 34cm^2. Calculate the area of triangle DEF from the picture.

The required Area of Triangle DEF is 51cm square.

Given that,

The triangles ABC=DEF

Then, height of ABC= height of DEF

By the given picture we have

CB = 9cm

FE =13.5cm

Area of ABC= 34cm square

According to the question,

The area of a triangle= [tex]\frac{1}{2}[/tex] × base × height,

Again, Area of ABC =  [tex]\frac{1}{2}[/tex] × base × height= 34cm square

=  [tex]\frac{1}{2}[/tex] × 9cm × height= 34cm square

=  [tex]\frac{9}{2}[/tex] cm × height= 34cm square

=  Height= [tex]\frac{34cmsquare}{\frac{9}{2} }[/tex]

= Height = [tex]\frac{68}{9}[/tex]cm.

The height of the triangle ABC is [tex]\frac{68}{9}[/tex]cm.

Therefore,

Area of DEF = [tex]\frac{1}{2}[/tex] × base × height

= [tex]\frac{1}{2}[/tex] × 13.5cm × ([tex]\frac{68}{9}[/tex])cm

= 51cm square

Therefore, the Area of Triangle DEF is 51cm square.

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Answer:

42

Step-by-step explanation:

= 10+8^3/16

= 10+512/16

= 10+32

= 42

The rental company to hat Oscar should use is the second company because it's cheaper.

The total amount charged for the first boat will be:

= 100 + 35h

where h = number of hours

= 100 + 35(8)

= 100 + 260

= $360

The amount charged for the second company will be:

= 50 × 8

= 400

Therefore, the rental company to hat Oscar should use is the second company because it's cheaper.

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Answer:

25 + 5x = 30 + 2x

At 5/3s of an hour is when the cost of both tubing companies are the same.

This is when the price of both companies both hit $33.33

Step-by-step explanation:

25 + 5x = 30 + 2x

move variables by subtracting

25 + 3x = 30

move constants by subtracting  

30 - 25 = 5

5 = 3x

x = 5/3

According to the question, in the gift exchange event. Tisha draws first gift and her friend Brandi second gift.

The total number of participating students is [tex]18[/tex].

To calculate the probability that Brandi and Tisha draw each other’s name is as follows:

Using conditional probability, the solution is as follows:

[tex]P(E) = \frac{1}{18}\frac{1}{17} = \frac{1}{306} = 0.3%[/tex]

The calculated percentage is [tex]0.3[/tex].

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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Pizza costing $24 is being delivered to Brian's home. The change $7.72 he get if he uses two $20 bills as payment.

Given that,

Pizza costing $24 is being delivered to Brian's home.

He pays the amount in addition to the 7% sales tax and 15% tip.

In addition, he pays the delivery price of $3, which is added on after tax and tip.

We have to find how much change does he get if he uses two $20 bills as payment.

To figure out the sales tax

$24×0.07=$1.68

To figure out the tip

$24×0.15=$3.6

The Total cost=$24+$1.68+$3.6+$3=$32.28

Now, To find change we have to add the Total cost and the bill

Change=2($20)-$32.28

Change=40-32.28

Change=$7.72

Therefore, The change $7.72 he get if he uses two $20 bills as payment.

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Here the conjecture we can made is :

The sum of interior angles i.e. ∠A and ∠B is equal to the exterior angle at C.

The exterior angle of any triangle is defined as the angle which is at the outside boundaries of that triangle. whereas, the interior angle is defined as the angle which is inside the triangle. In the other words if the triangle has the point within the angle it is in the interior of the angle , but if the point is outside then is it said to be in the exterior of the angle for that triangle.

In mathematics, the two angles are called as adjacent angles if they have a common vertex or we can say they are angle of a common vertex in the triangle.

we can define the adjacent angle as the angles which have common side and common vertex and they don't overlap.

According to the exterior angle property, if a side of a triangle is made, then the exterior angle formed is always equals to the sum of  two interior angles opposite to each other in the triangle.

Thus on the basis of exterior angle property we can make the conjecture that, "the measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles".

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Answer:

n=21

Step-by-step explanation:

3n-21=2n

subtract 3n from each side

-21=-1n

two negatives become a positive

Answer:

k = 1

This is because when g(x) = 8, f(x) = 8

and when g(x) = 2, f(x) = 2

and this continues throughout the graph

Answer:

k=12

t=8

Step-by-step explanation:

two equations from the question

1 k=t+6

2 (k-4)=(t-4)×2

develop these

3. k-4=2t-8

4. 2 times first equation

2k=2t+12

subtract 4 from 3

-k-4=-20

k=16

sub back in

t=10

Answer:

There is 2121.80 in the account after 2 years.

Step-by-step explanation:

Use the formula A = P(1 + r)^t  where P = initial amount, A = amount after t years and r = the rate (as a decimal).

So, for this problem:

Amount after 2 years = 2000(1 + 0.03)^2

= £2121.80

The expression that relates the measure of <1 and arcs QP and arcSP is expressed as m<1 = 1/2(arcQR+arcSP)

When two chords intersect inside a circle, the angle formed is half of the sum of the subtended arcs.

From the given diagram, the intercepted arcs are arcQR and arcSP and the measure of the interior angle is <1.

Using the theorem above, the expression that relates the measure of <1 and arcs QP and arcSP is expressed as:

m<1 = 1/2(arcQR+arcSP)

The measure of the angle <1 is equivalent to half the sum of arcQR and arcSP.

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Any sequence is termed as the arithmetic sequence when the common difference between two consecutive values are same.

In Arithmetic Progression, the difference between the two numerical orders is a fixed value (AP). Arithmetic Sequence is another name for it.

We'd come across a few particular words in AP that had been labeled as:

As shown below, the AP can also be defined in concepts of common differences.

Now, for the given question;

Let the initial term be 'a₁'.

Let the second term be 'a₂'.

Let the third term be 'a₃'.

And, consider the fourth term as 'a₄'.

The AP must have the equal common difference. So,

d = a₃ - a₂ or d = a₄ - a₃

When the value of the common difference 'd' is found same in any of the cases, it said to form an AP.

Therefore, for the sequence to be an arithmetic sequence in common difference must be equal.

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There is not enough evidence

An indicator of how much a group of numbers vary or are dispersed is the standard deviation. [1] When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.

For  1.5 moles substrate concentration per liter

Reaction ( n2 ) = 15 runs

average velocity ( x2 ) = 7.5 micromoles per 30 minutes

standard deviation ( s2 ) = 1.5

For 2.0 moles substrate concentration per liter

Reaction( n1 ) = 12 runs

(x1) = 8.8 micromoles on average per 30 minutes

standard deviation ( s1 )  = 1.2

Show Reason to believe that this increase in substrate conc causes an increase in mean velocity

Hypothesis test

H0 : μ1 - μ2 = 0.5

H1 : μ1 - μ2  > 0.5

significance level ( ∝) = 0.01

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The sum of the given finite series is 25

The summation notation means that we have to add the terms of the given series with n moves from the lower limit to the upper limit.

The given series is:

      [tex]\sum\limits^5_{n=1} {(2n-1)}[/tex]

In this series, the lower limit is n = 1 while the upper limit is n=5.

n = 1  ⇒ 2n - 1 =  2(1) -1 = 1

n = 2  ⇒ 2n - 1 = 2(2) -1 = 3

n = 3  ⇒ 2n - 1 = 2(3) -1 = 5

n = 4  ⇒ 2n - 1 = 2(4) -1 = 7

n = 5  ⇒ 2n - 1 = 2(5) -1 = 9

Hence,

[tex]\sum\limits^5_{n=1} {(2n-1)}=1+3+5+7+9[/tex]

We can evaluate the sum of the series directly, or by using the sum formula as follow:

S(n) = n/2 [a(1) + a(n)]

Substitute n = 5, a(1) =1, and a(n) = 9:

S(5) = 5/2 (1 + 9) = 25

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Answer:

1) y=5/4

2) y=−6

Step-by-step explanation:

Let's solve the equation step by step.

1) 2xy - x = 3

(2)(2)y - 2 = 3

4y - 2 = 3

4y−2=3

Step 1: Add 2 to both sides.

4y−2+2=3+2

4y=5

Step 2: Divide both sides by 4.

4y/4 = 5/4

y=5/4

2) 2y + xy = 6

2y−3y=6

Step 1: Simplify both sides of the equation.

2y−3y=6

2y+−3y=6

(2y+−3y)=6(Combine Like Terms)

−y=6

−y=6

Step 2: Divide both sides by -1.

−y/−1 = 6/−1

y=−6

Missing term i.e., the second term of the sequence is 5.

As the series is in an arithmetic sequence, so we have an equation

[tex]a_{n}[/tex] = a +(n-1)d

Where a = first number of the series

           n = number of term

           d= common difference

As we know the 3rd term of the sequence, so by this we can find the common difference.

So we have,

9 = 1 +(3-1)d

8=2d

d=4

common difference = 4

Now we have to find the 2nd term or the missing term of the sequence, so we have

[tex]a_{2}[/tex] = 1 +(2-1)4

   = 1+ 1×4

   = 1+4

   = 5

Therefore the 2nd term is 5.

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[tex]Answer:\ a_n=34-8n[/tex]

Step-by-step explanation:

26, 18, 10, 2

18-26=-8

10-18=-8

2-10=-8

This is an arithmetic progression:

[tex]a_n=a_1+(n-1)d,\\a_1=26\ \ \ \ \ d=-8\ \ \ \ n=1,\ 2,\ 3,\ 4\\a_n=26+(n-1)(-8)\\a_n=26+(n)(-8)+(-1)(-8)\\a_n=26-8n+8\\a_n=34-8n[/tex]

Answer:

-10

Step-by-step explanation:

Convert to improper fractions and do the math

-8/3 - 22/3  

-30/3

-10

Step-by-step explanation:

it looks like a smiley face

Answer: BC=17

Step-by-step explanation:

AC=AB+BC

27=10+BC

27-10=10-10+BC

BC=27-10

BC=17

Answer:

120

Step-by-step explanation:

We start with the equation:

[tex]\frac{1}{3}x-\frac{3}{8}x -\frac{7}{24}x =-40[/tex]

We need to set the fractions into equal denominations so we can sum them all together:

[tex]\frac{8}{24}x-\frac{9}{24}x -\frac{7}{24}x =-40\\[/tex]

Now sum the fractions:

[tex]\frac{8-9-7}{24}x=-40\\\\ \frac{-8}{24}x=-40[/tex]

Multiple both sides by 24 to eliminate denominator on left side of equation:

[tex]-8x=-960[/tex]

Divide both sides by -8 to get the value of x:

[tex]x=120[/tex]

In the context of this problem, the meaning of the y-intercept is: D. The average rate of change that is occurring is 1.03.

The average rate of change can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

In Mathematics, the y-intercept of any graph occurs at the point where the value of "x" is equal to zero (0). Similarly, the x-intercept refers to the point at which the graph of a function crosses the x-axis and the value of "y" is equal to zero (0).

In the context of this problem, we can reasonably infer and logically deduce that the meaning of the y-intercept is the average rate of change that is occurring is 1.03 while 500 represents the initial investment.

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Answer:

The better choice is a rebate of $75. You would save $3.75 more.

Answer: D

Step-by-step explanation:

The time exactly halfway between 42.60 seconds and 49.24 seconds is 45.92 seconds.

Halfway simply means the midpoint between two values. It is the distance between two values divided by two. It can also mean the average of the two values.

If the women's 400m world record is 42.60 seconds and the 16th fastest women's 400m runner ran it in 49.24 seconds, to find the exact halfway of these two records means to find the average of these two records of time. Add the two records of time and divide by two.

n = (42.60 + 49.24)/2

n = 91.84/2

n = 45.92 seconds

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