This table shows some values of an exponential function.
What is the function?

Answer:

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

Step-by-step explanation:

(x - [tex]\frac{5}{6}[/tex] )² = [tex]\frac{1}{36}[/tex] ( take square root of both sides )

x - [tex]\frac{5}{6}[/tex] = ± [tex]\sqrt{\frac{1}{36} }[/tex] = ± [tex]\frac{1}{6}[/tex] ( add [tex]\frac{5}{6}[/tex] to both sides )

x = [tex]\frac{5}{6}[/tex] ± [tex]\frac{1}{6}[/tex] , then

x = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

x = [tex]\frac{5}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{6}{6}[/tex] = 1

Answer:

see explanation

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 8x + 8y + 23 = 0

collect the x and y terms together and subtract 23 from both sides

x² - 8x + y² + 8y = - 23

using the method of completing the square

add ( half the coefficient of the x / y terms )² to both sides

x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16

(x - 4)² + (y + 4)² = 9 ← in standard form

with centre = (4, - 4 ) and r = [tex]\sqrt{9}[/tex] = 3

this is shown in graph b

The three side length that describes the triangle in the image attached below are: 5 cm, 12 cm, and 13 cm.

A triangle is a shape that has three sides. The sides can be measured using a ruler.

The sides of the triangle in the image shown have side lengths as measured by the ruler beside each of the sides, which are 5 cm, 12 cm, and 13 cm.

Therefore, the three side lengths of the triangle in the diagram are: 5 cm, 12 cm, and 13 cm.

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Answer:

60%

Step-by-step explanation:

So, this question is saying the bowls can be between a diameter of 6.95 and 7.05

Box 1, 3 and 5 are in this margin.

Box 2 and 4 are not.

3/5 boxes can be included.

3/5 is 6/10

6/10 is 60%

In 15 years, the average car releases 458.7 kilograms of nox.

We know that the average vehicle releases 1.39 grams per mile driven.

And, in average, that car drives 22,000 miles per year.

So in a year, a car releases:

M = (22,000)*1.39 g  = 30,580 g = 30.58 kg

In one year, the average car releases around 30.58 kilograms of nox.

Then in 15 years, the car releases 15 times that amount, then we have the product:

T = 15*30.58 kg = 458.7 kg

In 15 years, the average car releases 458.7 kilograms of nox.

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[tex]\sf Sine \ Rue : \ \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

Given following:

Solve for b (distance between school and mall):

[tex]\dashrightarrow \sf \dfrac{\sin 56}{38} = \dfrac{\sin 77}{b}[/tex]

[tex]\dashrightarrow \sf b= \dfrac{38\sin 77}{\sin 56}[/tex]

[tex]\dashrightarrow \sf b= 44.6615 \quad \approx \quad 45[/tex]

Answer:

a) 13

b) 1/3

c) -2

d) 1

Step-by-step explanation:

This is quite simple if you look at it from a different perspective. Imagine that when it says "f(2)" That you are plugging the number 2 in for every x on the right side of the equation:

For example:

f(x) = 3x + 7

f(2) = 3(2) + 7

f(2) = 6 + 7

f(2) = 13

________

f(-3) = 3x + 7

f(-3) = 3(-3) + 7

f(-3) = -9 + 7

f(-3) = 7 - 9 (This is just for those that hate negative values. You can rearrange the values as long as their sign is the same when you do move them. Ex: -14 + 6 - 4 + 9 == 9 + 6 - 14 - 4. I hope that makes sense.

f(-3) = -2

The other way is quite simple as well, if you look at it from a different perspective. Imagine that when it says "f(x) = 8" that you are changing the f(x) to the number 8:

For example:

f(x) = 8

f(x) = 3x + 7

8 = 3x + 7

8 - 7 = 3x

1 = 3x

x = 1/3

f(x)= 10

f(x) = 3x + 7

10 = 3x + 7

10 - 7 = 3x

3 = 3x

3/3 = x

1 = x

I hope this helps!

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ h=9 \end{cases}\implies V=\pi (12)^2(9)\implies V=1296\pi ~m^3[/tex]

A beam measuring 2 meters can support 172 kilograms

The variation is a direct variation.

So, we have:

w = kl

Where k is the constant of variation.

When l = 5, w = 430.

This means that:

430 = 5k

Divide both sides by 5

k = 86

So, we have:

w = 86l

When l = 2, we have:

w = 86 * 2

Evaluate

w = 172

Hence, a beam measuring 2 meters can support 172 kilograms

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Based on the result from the box plot, the number of blue marbles is equal to the median of the data set and this is equal to 40.

A boxplot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:

For this exercise, we would create a box plot (see attachment) for the marbles in a bag of 100 marbles. By critically observing the box plot, we can logically deduce that the number of blue marbles is equal to the median of the data set and this is given by:

Median = 4 × 10

Median = 40.

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Answer:

A 90 percent level can be obtained with a smaller sample, which usually translates into a less expensive survey. To obtain a 3 percent margin of error at a 90 percent level of confidence requires a sample size of about 750. For a 95 percent level of confidence, the sample size would be about 1,000.

Answer:

x = 14

Step-by-step explanation:

given f(x) = 2(3x - 5) and f(x) = 74 , then equating gives

2(3x - 5) = 74 ( divide both sides by 2 )

3x - 5 = 37 ( add 5 to both sides )

3x = 42 ( divide both sides by 3 )

x = 14

eden must run 2 3/8 laps to complete the race.

To calculate the laps that Eden is missing, we must perform the following operation:

We must take into account that he has already completed 7 laps and a segment of the eighth lap that is equivalent to 5/8, that is to say that he has 3/8 to complete the eighth lap.

On the other hand, once he completes the eighth lap, he will have 2 full laps left to finish the race. Due to the above, it can be stated that it is missing 2 3/8 laps.

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The value of k based on the information given will be k = 2.

It should be noted that the line of f(x) passes through the point (-4, 0) and (0, 4). The line of g(x) goes through (-2, 0) and (0, 4).

The slope of x will be:

= (4 - 0)/(0 + 4)

= 4/4

= 1

By using slope point form, y = kx + 4.

Substitute x = 2.

g(-2) = -2k + 4 = 0

2k = 4

k = 4/2 = 2

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The probability you spin something larger than 10 will be 1  /  2.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The given data is:-

The probability will be calculated as:-

Total numbers = 8

Numbers greater then 10 are = 13 , 16 , 22 , 42 = 4

Probability  =  4  /  8  =  1  /  2

Therefore the probability you spin something larger than 10 will be 1  /  2.

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Answer:

yes

Step-by-step explanation:

Yes.

The graph of y = 2x - 2 is a straight line sloping up to the right.

It passes the vertical line test, so it is a function.

Answer:

true

Step-by-step explanation:

The statement is true because every graph associated a unique x-value for each y - value

The probability that he would have done at least this well if he had no ESP is 0.99979

To determine the probability, we need to first find the probability of doing well with ESP.

The probability of having 20 correct answers out of 23 coin flips is:

[tex]\mathbf{=(\dfrac{1}{2})^{20}}[/tex]

Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:

[tex]\mathbf{=(\dfrac{1}{2})^{3}}[/tex]

There are [tex](^{23}_{20})[/tex] = 1771 ways to get 20 correct answers out of 23.

Therefore, the probability of doing well with ESP is:

[tex]\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}[/tex]

= 0.00021

The probability that he would have at least done well if he had no ESP is:

= 1 - 0.00021

= 0.99979

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The number of acorns that each animal hid is 48

An equation is formed when two algebraic expressions are equated by an equal sign.

It is asked to calculate the number of acorns that each animal hid.

Total number of acorns hid  =  number of acorns hid per tree * number of trees    

Let   T be the number of trees chipmunk used

For chipmunk:    = 3*T

For squirrel:   = 4*(T-4)

 As both the animals hid same number of acorns.

    3T = 4(T-4)      

    3T = 4T - 16      

      16 = T

Therefore the chipmunk hid 16 * 3 = 48 acorns

and the squirrel hid 4(16-4) = 48 acorns.

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This  is an equilateral triangle, therefore, all the angles  are 60 degrees.

3 times  60 is  180.

180 is the answer

What is the sentence and what are the questions. Until I know I can't help. But I should be able to answer if you can tell me

Answer: rectangle

Step-by-step explanation:

The options imply the figure is a parallelogram. Furthermore, we can tell that not all the sides are congruent, so we can rule out the possibility that it is a rhombus or a square.

To determine if it is a rectangle, we can use the slope formula to determine if there is a pair of perpendicular sides. If this is the case, then this will be a parallelogram with a right angle, making it a rectangle.

[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC}[/tex]

So, the most specific classification is a rectangle

5 blue, 4 red = 9 total

Probability (Blue, Blue)  = 5/9 x 5/9 = 25/81 = 0.30864

Probability (Red, Red) = 4/9 x 4/9 = 16/81 = 0.19753

Probability (Blue,Blue) or (Red,Red) = 25/81 + 16/81 = 41/81 = 0.506173

Fraction answer = 41/81

Decimal answer = 0.506173 (round off as needed)

Answer:

[tex]r \: = \: \boxed{ \bold{\frac{2}{3} }}[/tex]

Step-by-step explanation:

[tex]r \: = \: \frac{36}{54} \\ \\ r \: = \: \frac{24}{36} \\ \\ r \: = \: \frac{16}{24} [/tex]

[tex]r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} [/tex]

Since the ratio is the same, that is the common ratio.

[tex]m_{\overline{AB}}=\frac{0-0}{1-5}=0\\m_{\overline{CD}}=\frac{2-2}{3-7}=0\\\\\therefore \overline{AB} \parallel \overline{CD} \text{ because } m_{\overline{AB}}=m_{\overline{CD}}[/tex]

[tex]m_{\overline{BC}}=\frac{2-0}{7-5}=1\\m_{\overline{AD}}=\frac{2-0}{3-1}=1\\\\\therefore \overline{BC} \parallel \overline{AD} \text{ because } m_{\overline{BC}}=m_{\overline{AD}}[/tex]

As ABCD has two pairs of opposite parallel sides, ABCD is a parallelogram.

Answer:

Random sampling

Step-by-step explanation:

Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling.

Answers: sin(2∅) = 120/169,  cos(2∅) = 119/169, tan(2∅) = 120/119

Trigonometric functions are used to establish the relationship between the sides and the angles of a right angle triangle.

Analysis:

If cos∅ = adjacent/hypotenuse =  12/13,

Then, opposite of the right angled triangle = [tex]\sqrt{13^{2} - 12^{2} }[/tex] = 5

sin∅ = 5/13, cos∅ = 12/13, tan∅ = 5/12

sin(2∅) = 2sin∅cos∅ = 2(5/13)(12/13) = 120/169

cos(2∅) = [tex]cos^{2}[/tex]∅ - [tex]sin^{2}[/tex]∅ = [tex](\frac{12}{13}) ^{2}[/tex] - [tex](\frac{5}{13} )^{2}[/tex] = 144/169 - 25/169 = 119/169

tan(2∅) = sin(2∅) / cos(2∅)  = 120/169 ÷ 119/169 = 120/119

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