Use the negative exponent rule to simplify. 10^5 x 10^-10. Use only positive exponents for expression.

Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)

\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios

\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

Dots sold 65 T-shirts and 13 shorts

let the x represent the number of T-shirts and y and shorts

7x + 9y= 572.......equation 1

x= 5y........equation 2

substitute 4y for x in the equation

7(5y) + 9y = 572

35y  + 9y= 572

44y= 572
y= 572/44

y= 13

substitute 13 for y in equation 2

x= 5(13)

x= 65

Hence there 65 T-shirts and 13 shorts

Read more on equation here

https://brainly.com/question/22243794

#SPJ1

The solution to the equations are b = 15, b = 22, c = 21 and n = 28

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

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Next, we collect the like terms in each of the equation

This gives

b = 31 - 16

b = 50 - 28

c = 54 - 33

n = 52 - 24

Lastly, we evaluate the like terms

b = 15

b = 22

c = 21

n = 28

The above are the solutions to the equations

Read more about equations at

https://brainly.com/question/148035

#SPJ1

Question

Solve the following equations:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

For given  regression model, the number 59.89 in the table tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

In this question we have been given a summary of regression model.

We need to explain the meaning of the number 59.89 in the table.

For given regression model, to view the results of the model, we can use the summary() function in R programming.

In given summary consider the 'Coefficients' table.

The first row gives the estimates of the y-intercept, and the second row gives the regression coefficient of the model.

The 'Estimate' column is the estimated effect, also called the regression coefficient or r² value.

The number 59.89 in the table is coefficient for IsSandwich.

This number tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

Therefore, the meaning of the number 59.89 in the table: for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

Learn more about the regression model here:

https://brainly.com/question/14983410

#SPJ4

The complete question is as shown in the following image

Answer:

D

Step-by-step explanation:

A is impossible.

the absolute value of something is always a positive number. the negative sign before it makes it an always negative number. so, this can never be equal to +5.

B is impossible for the same reasons.

the absolute value is always positive and can never be equal to -5.

C is impossible again for the same reasons.

the negative absolute value of x is always negative. subtracting 2 from that makes the result even more negative. this can never be equal to +5.

D is the only fitting option.

we have two extreme points x = -3 and x = 7.

putting them into the equation gives us for x = -3

-|-3 - 2| = -|-5| = -5 => correct

and for x = 7

-|7 - 2| = -|5| = -5 => correct

The correct answer is -|x - 2| = -5

A. The graph of the absolute value function is V-shaped, with the features given as follows:

B. The transformation is that the function was shifted right two units, hence the features are given as follows:

The absolute value function, with vertex (h,k), is defined as follows:

y = |x - h| + k.

The features of the function are given as follows:

For the first item, the function is |x + 3|, hence we just have to identify the features.

For the second function, the definition if h(x) = |x - 2|, with vertex at (2,0), meaning that the function was shifted two units right from the parent absolute value function y = |x|. The shift just changes the turning point of the graph, not altering domain and range.

More can be learned about absolute value functions at https://brainly.com/question/3381225

#SPJ1

The transformed equation of \(y = x^{3}\) is \(y = -\frac{1}{7} (x + 8)^{3}\).

Given equation ;  \(y = x^{3}\)

Applying the given transformations, we have:

To have a vertical compression by a factor of  \(\frac{1}{7}\), we need to multiply the function by  \(\frac{1}{7}\). So, we have:

\(y =\)  \(\frac{1}{7}\) \(x^{3}\)

To have a horizontal shift by 8 units to the left, we need to add 8 to x. So, we have:

\(y = \frac{1}{7} (x + 8)^{3}\).

Lastly, to have a reflection over the x-axis, we need to multiply the function by −1. So, we have:

\(y = -\frac{1}{7} (x + 8)^{3}\).

Therefore, the transformed equation is  \(y = -\frac{1}{7} (x + 8)^{3}\).

Learn more about transformation here;

https://brainly.com/question/2689696

#SPJ4

Answer:

8 + 3x ≤ 20

Step-by-step explanation:

Given

2 Games = $8

Additional Game = $3

Amount = $20

Required

Determine the inequality that represents the number of games

From the question, we understand that the minimum number of games that can be played is 2.

So, the expression can be:

Cost of 2 games + Cost of additional games ≤ Amount

This gives:

8 + 3 * x ≤ 20

Where x represents the additional number of games

By simplifying the expression, we have:

8 + 3x ≤ 20

When three college students are randomly selected, the probability that ALL three buy their textbooks online is 0.227

The probability that at least one purchases their textbooks online is 1.

As per the question the probability of students purchase their textbooks online 61%.

\(=\frac{61}{100}\)

p = 0.61.

So, failure = 1 - 0.61 = 0.39

q = 0.39

When 3 students are selected(n = 3)

We know that, \($$p(x)={ }^n c_x p^x q^{n-x}$$\)

So, probability that all of them to purchase

\($$\begin{aligned}&(x=3) \\& p(3)={ }^3 c_3(0.61)^3(0.39)^{3-3} \\& p(3)=0.22698\end{aligned}$$\)

When 5 students are selected (n = 5)

And probability that at least one purchases books online

\(=P(x=1)+P(x=2)+P(x=3)$ $+P(x=4)+P(x=5)$\)

Now we know that probability of all equal to 1.

\(P(0)+P(1)+P(2)+P(3)+P(4)+P(5)=1\)

So, we can simply write

\($$\begin{aligned}P & =1-p(x=0)+p(x=1) \\& =1-\left[{ }^5 C_0(0.61)(0.35)^{50}+{ }^5 C_1(0.61)^1(0.39)^{5-1}\right] \\& =1-0.00902-0.07056 \\P& =0.92042\end{aligned}$$\)

For more questions on probability

https://brainly.com/question/29161646

#SPJ4

As a percentage, a card at random 5, 6, 7, 8 9, 7.5, 6.42, 5.62. Per cent is derived from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century.

Therefore,

45/5 = 9

45/6 = 7.5

45/7 = 6.42

45/8 = 5.62

To learn more about percentage, refer to:

https://brainly.com/question/24877689

#SPJ1

The representation that is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time is a Line Plot

A line plot, or dot plot/strip plot, is a simple visual method of displaying data that shows the spread of values on a horizontal scale. A frequent application of it is to graphically display the occurrence or spread of a solitary factor.

A line plot generally displays individual data points as a small dot or short line segment along a specific axis, usually the horizontal axis. The location of the dot or line segment indicates the numerical value of the data point. Usually, the up and down axis showcases the frequency or the number of times a particular value occurs.

With this type of Table, the top is always X and the bottom is always Y.

Read more about line plots here:

https://brainly.com/question/27246403

#SPJ1

Answer:

(5.240 ; 8.760)

Step-by-step explanation:

Given :

Sample mean, xbar = 7

Standard deviation, s = 2.29

Sample size, n = 9

95% confidence interval for the population mean :

Confidence interval :

Xbar ± Margin of error

Margin of Error = Tcritical * s/sqrt(n)

Tcritical at 0.05 ; df = 8 = 2.306

Margin of Error = 2.306 * 2.29/sqrt(9)

Margin of Error = 1.760

Lower boundary = (7 - 1.760) = 5.240

Upper boundary = (7 + 1.760) = 8.760

(5.240 ; 8.760)

The value of x is 24 and different angles of hexagon will be -

A = 160

B = 142

C = 120

D = 156

E = 31

F = 111

An angle is a geometric shape that is defined as the amount of rotation that occurs between two straight lines or planes. Angles are measured in degrees, with 360° representing a full circle.

We need to apply the inverse tangent function to determine the angle at which the sun strikes the flagpole. We are aware that the triangle's adjacent side is 42 feet long and its opposite side is 25 feet tall (the height of the flagpole) (the length of the shadow).

Given the figure is hexagon,

the sum of angles of a hexagon is 720,

Upon adding the given angles,

mA = (7x-8)°

mB (4x+46)°

mC = (5x)

mD = (6x+12)°

mE = (x+7)°

mF = (5x-9)°

⇒ 7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720

⇒ 28x + 48 = 720

⇒ 28x = 672

⇒ x = 24

Therefore, the angles will be -

A = 160

B = 142

C = 120

D = 156

E = 31

F = 111

To know more about angle click-

https://brainly.com/question/28769265

#SPJ1

Answer:

2.275%

Step-by-step explanation:

We solve this question using z score formula

z = (x-μ)/σ,

where

x is the raw score = 70 mph

μ is the population mean = 100 mph

σ is the population standard deviation = 15 mph

z score = 70 - 100/15

z score = -30/15

z score = - 2

Determining the Probability value from Z-Table:

P(x ≤ 70) = P(x < 70)

= P(z = -2)

= 0.02275

Hence the probability of the player's serve that are less than 70 mph is 0.02275

Converting it to percentage

= 0.02275 × 100

= 2.275%

Therefore, the percentage of the player's serve speeds that are less than 70 mph is = 2.275%

A geometric sequence is characterized with a common ratio

The common ratio and the next three terms

Given the first three terms, the common ratio (r) is:

\(\mathbf{r = \frac{T_2}{T_1}}\)

While the nth term is:

\(\mathbf{T_n = T_1 \times r^{n-1}}\)

So, we have:

1. 972, 324, 108, …

The common ratio (r) is:

\(\mathbf{r = \frac{324}{972}}\)

\(\mathbf{r = \frac{1}{3}}\)

The next three terms are:

\(\mathbf{T_4 = 972 \times (\frac 13)^3 = 36}\)

\(\mathbf{T_5 = 972 \times (\frac 13)^4 = 12}\)

\(\mathbf{T_6 = 972 \times (\frac 13)^5 = 4}\)

So,

\(\mathbf{r = \frac{1}{3}\ and\ \mathbf{n = 36, 12, 4}}\)

2. -3, 12, -48, …

The common ratio (r) is:

\(\mathbf{r = \frac{12}{-3}}\)

\(\mathbf{r = -4}\)

The next three terms are:

\(\mathbf{T_4 = -3 \times (-4)^3 = 192}\)

\(\mathbf{T_5 = -3 \times (-4)^4 = -768}\)

\(\mathbf{T_6 = -3 \times (-4)^5 = 3072}\)

So,

\(\mathbf{r = -4 \ and\ n = 192, -768, 3072}\)

3. 0.1, 0.5, 2.5, …

The common ratio (r) is:

\(\mathbf{r = \frac{0.5}{0.1}}\)

\(\mathbf{r = 5}\)

The next three terms are:

\(\mathbf{T_4 = 0.1 \times (5)^3 = 12.5}\)

\(\mathbf{T_5 = 0.1 \times (5)^4 = 62.5}\)

\(\mathbf{T_6 = 0.1 \times (5)^5 = 312.5}\)

So,

\(\mathbf{r = 5 \ and\ n = 12.5, 62.5, 312.5}\)

4. 10 000, 1 000, 100, …

The common ratio (r) is:

\(\mathbf{r = \frac{1000}{10000}}\)

\(\mathbf{r = \frac{1}{10}}\)

The next three terms are:

\(\mathbf{T_4 = 10000 \times (\frac{1}{10})^3 = 10}\)

\(\mathbf{T_5 = 10000 \times (\frac{1}{10})^4 = 1}\)

\(\mathbf{T_6 = 10000 \times (\frac{1}{10})^5 = \frac{1}{10}}\)

So,

\(\mathbf{r = \frac{1}{10} \ and\ n = 10, 1, \frac{1}{10}}\)

5. -4, 4, -4, ...

The common ratio (r) is:

\(\mathbf{r = \frac{4}{-4}}\)

\(\mathbf{r = -1}\)

The next three terms are:

\(\mathbf{T_4 = -4 \times (-1)^3 = 4}\)

\(\mathbf{T_5 = -4 \times (-1)^4 = -4}\)

\(\mathbf{T_6 = -4 \times (-1)^5 = 4}\)

So,

\(\mathbf{r = -1 \ and\ n = 4,-4,4}\)

The first 2 terms

\(6.\ \mathbf{a_1 =2 , r = 4}\)

The nth term is:

\(\mathbf{a_n = a_1 \times r^{n-1}}\)

So, the second term is:

\(\mathbf{a_2 = 2 \times 4 = 8}\)

So, we have:

\(\mathbf{n = 2, 8}\)

\(7.\ \mathbf{a_1 =5, r = -\frac 13}\)

The nth term is:

\(\mathbf{a_n = a_1 \times r^{n-1}}\)

So, the second term is:

\(\mathbf{a_2 = 5 \times -\frac 13 = -\frac 53}\)

So, we have:

\(\mathbf{n = 5, -\frac 53}\)

The nth term

\(\mathbf{8.\ a_1 = 3, r = 5}\)

The 7th is calculated using:

\(\mathbf{a_7 = a_1 \times r^6}\)

\(\mathbf{a_{7} = 3 \times 5^{6}}\)

\(\mathbf{a_7 = 46875}\)

\(\mathbf{9.\ a_1 = 0, r = 4}\)

The 30th is calculated using:

\(\mathbf{a_{30} = a_1 \times r^{29}}\)

\(\mathbf{a_{30} = 0 \times 4^{29}}\)

\(\mathbf{a_{30} = 0}\)

The number of term

\(\mathbf{10.\ n = 1,2,4,8....}\)

\(\mathbf{a_n = 64}\)

\(\mathbf{a_1 = 1}\)

Start by calculating the common ratio (r)

\(\mathbf{r = \frac 21}\)

\(\mathbf{r = 2}\)

So, the nth term is:

\(\mathbf{a_n = a_1 \times r^{n-1}}\)

Substitute known values

\(\mathbf{64 = 1 \times 2^{n-1}}\)

\(\mathbf{64 = 2^{n-1}}\)

Express 64 as 2^6

\(\mathbf{2^6 = 2^{n-1}}\)

Cancel out 2 on both sides

\(\mathbf{6 = n-1}\)

Add 1 to both sides

\(\mathbf{7 = n}\)

Rewrite as:

\(\mathbf{n = 7}\)

Hence:

64 is 7th term

Read more about geometric sequence at:

https://brainly.com/question/18109692

Answer:

263347200

Step-by-step explanation:

Mark branliest please

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer:

1/12

Step-by-step explanation:

probability of flipping tails is 1/2

probability of rolling 6 is 1/6

1/2 x 1/6 = 1/12

The study described is a randomized experiment.

A randomized experiment is a typical experimental study design. It is a study design in which the researcher or investigator is in complete control of the research environment. For example, an investigator may wish to assess the effects of certain treatments on some experimental units.

The investigator decides the type of treatment, the type of experimental unit to use, and the allocation and assessment procedures of the treatments and effects, respectively, while in an observational study, the researcher or investigator is usually a passive observer as he only observes and analyses facts and events as they occur naturally.

In experimental studies, the researcher is in complete control of the exposure, and the result should therefore provide stronger evidence of an association or lack of association between exposure and a health problem than would an observational study.  

To know more about randomized experiment, here

https://brainly.com/question/10050306

#SPJ4

"Determine whether the study described below is a randomized experiment or an observational study.

A medical researcher wants to determine whether exercise can lower blood pressure. She recruits 100 people with high blood pressure to participate in the study. She assigns a random sample of 50 of them to pursue an exercise program that includes daily swimming and jogging. She assigns the other 50 to refrain from vigorous activity. She measures the blood pressure of each of the 100 individuals both before and after the study."--

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

33 is the answer for this ez math

Answer:

2,322,775

Step-by-step explanation:

Given a1 = 4 and ai =ai-1 +11

when i = 2

a2 = a2-1+11

a2 = a1+11

a2 = 4+11

a2 = 15

when i = 3

a3 = a2+11

a3 = 15+11

a3 = 26

The sequence formed by a1, a2, a3... is am arithmetic sequence as shown;

4, 15, 26...

Sum of nth term of an arithmetic sequence = n/2{2a+(n-1)d}

a is the first term = 4

d is the common difference = 15-4 = 26-15 = 11

n is the number of terms.

Since we are to find the sum of the first 650 terms in the sequence, n = 650

S650 = 650/2{2(4)+(650-1)11}

S650 = 325{8+(649)11}

S650 = 325(8+7,139)

S650 = 325×7147

S650 = 2,322,775

Answer:

1 and two-thirds yards

Step-by-step explanation:

5⅓ = 3⅔ + y. Subtract 3⅔ from both sides.

It may be useful to use improper fractions.

16/3 – 11/3 = y

5/3 = y

5/3 is equivalent to 1⅔

Answer:

First one

Step-by-step explanation:

Answer:

58,21    ≤   μ  ≤   61,79

Step-by-step explanation:

Normal Distribution

Poputation size        n = 41

Population mean         X  = 60

Population standard deviation    σ = 7

Question is: Confidence Interval 90 % ??

As Confidence Interval is 90 %   then  α  = 10 %

And as we are dealing with a two tail test

α/2  = 0,05

We look in Z table for values for  α/2  = 0,05  and find

z(α/2)  =  - 1,64      and    z(α/2) =  1,64

Then

Confidence Interval is

X - Zα/2 * σ/√n   ≤  μ  ≤  X + Zα/2 * σ/√n

60 - ( 1,64 ) * 7/√41  ≤   μ  ≤  60 + ( 1,64 ) * 7/√41

60 -  1,64 * 1,09375   ≤   μ  ≤  60 +  1,64 * 1,09375

60 - 1,79375    ≤   μ  ≤  60 +  1,79375

58,21    ≤   μ  ≤   61,79

Answer:

4X+2

Step-by-step explanation:

Since there is a negative in front of (4X+5), this will change the signs of both 4x and +5 to (-4X) and (-5) respectively.

This will make the equation look like as follows:-

8X +7 - 4X- 5

Thus on solving we get:-

8X- 4X +7 - 5

= 4X +2

-1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

To determine the value of "a" for which the function f(x) is continuous at x = 1, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 1 are equal, and if the value of f(x) at x = 1 is equal to these limits.

First, let's calculate the left-hand limit of f(x) as x approaches 1. For x < 1, the function is given by f(x) = (ax² - 1). To find the left-hand limit, we substitute x = 1 into this expression:

lim(x→1-) f(x) = lim(x→1-) (ax² - 1) = a(1²) - 1 = a - 1.

Next, let's calculate the right-hand limit of f(x) as x approaches 1. For x > 1, the function is given by f(x) = (a(x² - 2x + 1)). Substituting x = 1 into this expression, we have:

lim(x→1+) f(x) = lim(x→1+) (a(x² - 2x + 1)) = a(1² - 2(1) + 1) = a(1 - 2 + 1) = a.

For the function f(x) to be continuous at x = 1, the left-hand limit and the right-hand limit should be equal. Therefore, we have:

a - 1 = a.

To solve this equation for "a," we subtract "a" from both sides:

-1 = 0.

Since -1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

for such more question on equation

https://brainly.com/question/17482667

#SPJ8

Answer:

  D)  9 square units

Step-by-step explanation:

The squared term will always be non-negative, so the least it can be is zero (for x=3). The squared term is subtracted from 9, so the most the function value can be is 9.

The maximum area of the rectangle is 9 square units.

Answer:

9 square units

Step-by-step explanation:

Answer: plot one at -1 and the other at 5

Step-by-step explanation:

The Vertical intercept (0, 1/2)

The sums are 48, 52, 39, and 50

According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.

Given here: The addition of three numbers

When adding, always line up the addends, the two numbers being combined, one on top of each other according to their place values. Add the numbers in the ones column first, then the tens column, and finally the hundreds column, to get the sum, or the total.

1) \(24+14+10=\bold{48}\)

2) \(17+25+10=\bold{52}\)

3) \(16+13+10=\bold{39}\)

4) \(26+14+10=\bold{50}\)

Thus the sums of the respective equations gives 48, 52, 39, and 50 respectively

Learn more about the BODMAS rule here:

brainly.com/question/29795897