Jina wants to measure the width of a river. She marks off two right triangles, as shown in the figure. The base of the larger triangle has a length of 56m, and the base of the smaller triangle has a length of 26m. The height of the smaller triangle is 20.9m. How wide is the river? Round your answer to the nearest meter.

Answer:

c = 730cm

Step-by-step explanation:

The first thing we would do is to draw the diagram using th given information.

Find attached the diagram.

a = 714 cm

the measure of angle A = 78°

To determine c, we would apply sine rule. This is because we know the opposite and we are to determine the hypotenuse

sin78 = opposite/hypotenuse

sin 78 = 714/c

c = 714/sin 78 = 714/0.9781

c= 729.99

c≅ 730 cm ( nearest cm)

Answer:

It's written as

[tex]6.83 \times {10}^{ - 2} [/tex]

Hope this helps you

Answer:

6.83 × 10 -2

hopefully this helped :3

Answer:

Yes.

Step-by-step explanation:

In the future, simply plug both equations into Desmos.

Answer:

1. 77520

2. [tex]P_1[/tex] = 0.0017

3. [tex]P_2[/tex] = 0.0019

4. [tex]P_3[/tex] = 0.9981

5. [tex]P_4[/tex] = 0.2036

Step-by-step explanation:

The number of ways or combinations in which we can select x elements from a group of n can be calculated as:

[tex]nCx = \frac{n!}{x!(n-x)!}[/tex]

So, there are 77520 selections that result in all 7 workers coming from the day shift. It is calculated as:

[tex]20C7 = \frac{20!}{7!(20-7)!}=77520[/tex]

At the same way, the total number of selections of 7 workers from the 45 is 45C7, so the probability that all 7 selected workers will be from the day shift is:

[tex]P_1=\frac{20C7}{45C7} =0.0017[/tex]

The probability that all 7 selected workers will be from the same shift is calculated as:

[tex]P_2=\frac{20C7+15C7+10C7}{45C7} =0.0019[/tex]

Because the consultant can select all workers from the day shift (20C7) or can select all workers from the swing shift (15C7) or can select all workers from the graveyard shift (10C7).

On the other hand, the probability that at least two different shifts will be represented among the selected workers is the complement of the probability that all 7 selected workers will be from the same shift. So it is calculated as:

[tex]P_3 = 1- P_2=1 - 0.0019 = 0.9981[/tex]

Finally, the probability that at least one of the shifts will be un-represented in that sample of workers is:

[tex]P_4=\frac{25C7+30C7+35C7}{45C7} =0.2036[/tex]

Where 25C7 is the number of ways to select all 7 workers from swing or graveyard shift, 30C7 is the number of ways to select all 7 workers from day or graveyard shift and 35C7 is the number of ways to selects all 7 workers from day shift and swing shift.

Answer:

A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]

Step-by-step explanation:

Given A=  [tex]\left[\begin{array}{cc}5&25\\1&4\end{array}\right] \left[\begin{array}{cc}41&6\\20&2\end{array}\right][/tex] = B

Finding A*B means multiplying the first row with the first column and first row with the second column would give the first row elements. The second ro0w elements are obtained by multiplying the second row with the 1st column and second row with the second column.

so A*B= [tex]\left[\begin{array}{cc}5*41+ 25*20&5*6 + 25*2\\ 1*41+4*20 & 1*6+ 4*2\end{array}\right][/tex]

Now multiply and add the separate elements of the matrix A*B=

[tex]\left[\begin{array}{cc}205+500&30+50\\41+80&6+8\end{array}\right][/tex]

A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]

b. The 1st element of the 1st row shows the salaries of the managers and 2nd element of the 1st row the salaries of associates at the restaurant . The second row 1 st element shows the benefits of the managers and 2nd element the benefits of the associates at the food truck.

c. The total cost of salaries for all employees (managers and associates) at the restaurant = 705 + 80 = 785

Total cost of benefits for all employees at the food truck= 121 + 14= 135

━━━━━━━☆☆━━━━━━━

▹ Answer

Answer = b. 13/5

▹ Step-by-Step Explanation

|4 - 5| ÷ 9 × 3³ - 2/5

|-1| ÷ 9 × 3³ - 2/5

1 ÷ 9 × 3³ - 2/5

1/9 × 3³ - 2/5

1/3² × 3³ - 2/5

3 - 2/5

Answer = 13/5

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

[tex] \boxed{\sf b. \ \frac{13}{5}} [/tex]

Step-by-step explanation:

[tex] \sf Simplify \: the \: following: \\ \sf \implies \frac{ |4 - 5| }{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf 4 - 5 = - 1 : \\ \sf \implies \frac{ | - 1| }{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf Since \: - 1 \: is \: a \: negative \: constant, \: |-1| = 1: \\ \sf \implies \frac{1}{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf {3}^{3} = 3 \times {3}^{2} : \\ \sf \implies \frac{ \boxed{ \sf 3 \times {3}^{2}} }{9} - \frac{2}{5} \\ \\ \sf {3}^{2} = 9 : \\ \sf \implies \frac{3 \times 9}{9} - \frac{2}{5} \\ \\ \sf \frac{9}{9} = 1 : \\ \sf \implies 3 - \frac{2}{5} [/tex]

[tex] \sf Put \: 3 - \frac{2}{5} \: over \: the \: common \: denominator \: 5 : \\ \sf \implies 3 \times \frac{5}{5} - \frac{2}{5} \\ \\ \sf \implies \frac{3 \times 5}{5} - \frac{2}{5} \\ \\ \sf 3 \times 5 = 15 : \\ \sf \implies \frac{ \boxed{ \sf 15}}{5} - \frac{2}{5} \\ \\ \sf \implies \frac{15 - 2}{5} \\ \\ \sf 15 - 2 = 13 : \\ \sf \implies \frac{13}{5} [/tex]

Answer:

The answer is b=0 or b=9.085603

The equation is solved and the perfect squares are removed from the square root and A = b²√( 30b )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = √( 30b⁵ )

On simplifying the equation , we get

We can simplify the given expression by breaking down the number inside the square root into its prime factors:

30b⁵ = 2 x 3 x 5 x b⁵

Since we are looking to remove all perfect squares, we can remove the factors of 2 and 3, which are the only perfect squares present in the prime factorization of 30. This leaves us with:

30b⁵ = 2 x 3 x 5 x b⁵

= 2 x 3 x 5 x b⁴ x b

= 30b⁴ x b

Therefore, we can simplify the original expression as:

√(30b⁵) = √(30b⁴ x b) = √(30b⁴) x √b

A = b²√30 x √b

Hence , the expression √(30b⁵) simplifies to A = b²√30 x √b

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Answer:

The principal amount is $10160

Step-by-step explanation:

Given; Simple interest, I = 7620

Rate, R = 6.25

Time, T = 12

Principal, P =?

The formula for simple interest, I is;

[tex]I = \frac{PRT}{100}[/tex]

Making P the subject of formula;

[tex]P = \frac{I100}{RT}[/tex]

[tex]P = \frac{7620 *100}{6.25*12}[/tex]

[tex]P = \frac{762000}{75}\\P = 10160[/tex]

Therefore, the principal amount is $10160

Answer:

10000

Step-by-step explanation:

If an amount of money, P, called the principal, is invested for a period of t years at an annual interest rate r, the amount of simple interest, I, earned is given by

I=PrtwhereIPrt=interest=principal=rate=time

The following information is given.

Irt=$7,620=0.0635=12 years

Substituting the given information into the simple interest formula and solving for P gives

7,6207,620=(P)(0.0635)(12)=0.762P

Dividing both sides by 0.762, we have

P=7,6200.762=10,000

Thus, the principal amount of the bond was $10,000.

Answer:

c. there might not be any causal relationship between x and y.

Step-by-step explanation:

A correlation can be defined as a numerical measure of the relationship between existing between two variables (x and y).

In Mathematics and Statistics, a group of data can either be negatively correlated, positively correlated or not correlated at all.

1. For a negative correlation: a set of values in a data increases, when the other set begins to decrease. Here, the correlation coefficient is less than zero (0).

2. For a positive correlation: a set of values in a data increases, when the other set also increases. Here, the correlation coefficient is greater than zero (0).

3. For no or zero correlation: a set of values in a data has no effect on the other set. Here, the correlation coefficient is equal to zero (0).

If two variables, x and y, have a very strong linear relationship, then there might not be any causal relationship between x and y.

A causal relation exists between two variables (x and y), if the occurrence of the first causes the other; where, the first variable (x) is referred to as the cause while the second variable (y) is the effect.

A strong linear relationship exists between two variables (x and y), if they both increases or decreases at the same time. It usually has a correlation coefficient greater than zero or a slope of 1.

Hence, if two variables, x and y, have a very strong linear relationship, then there might not be any causal relationship between x and y.

Answer:

Hope this helps you

Answer:

Step-by-step explanation:

3x2−5x−2=0

For this equation: a=3, b=-5, c=-2

3x2+−5x+−2=0

Step 1: Use quadratic formula with a=3, b=-5, c=-2.

x= (−b±√b2−4ac )2a

x= (−(−5)±√(−5)2−4(3)(−2) )/2(3)

x= (5±√49 )/6

x=2 or x= −1 /3

Answer:

x=2 or x= −1/ 3

The solutions to the equation are x = -1/3 and x = 2.

Here are the steps on how to solve [tex]3x^{2}[/tex] – 5x – 2 = 0:

First, we need to factor the polynomial. The factors of 3 are 1, 3, and the factors of -2 are -1, 2. The coefficient on the x term is -5, so we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).

Next, we set each factor equal to 0 and solve for x.

(3x + 1)(x - 2) = 0

3x + 1 = 0

3x = -1

x = -1/3

x - 2 = 0

x = 2

Therefore, the solutions to the equation [tex]3x^{2}[/tex] – 5x – 2 = 0 are x = -1/3 and x = 2.

Here is the explanation for each of the steps:

Step 1: In order to factor the polynomial, we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).

Step 2: We set each factor equal to 0 and solve for x. When we set 3x + 1 equal to 0, we get x = -1/3. When we set x - 2 equal to 0, we get x = 2. Therefore, the solutions to the equation are x = -1/3 and x = 2.

Learn more about equation here: brainly.com/question/29657983

#SPJ2

Answer:

Equilateral

Acute

Step-by-step explanation:

The sides are all equal as indicated by the lines on each side - Equilateral

The angles are all equal by the angle marks  180/3 = 60 which is less than 90 degrees.  This makes the angles acute

Replace x with 2 and solve:

2^2 + 4(2) = 4 + 8 = 12

Replace x with 3 and solve:

3^2 + 4(3) = 9 + 12 = 21

The difference between the two answers is : 21 -12 = 9

The difference between the two inputs is 3-2 = 1

The rate of change is the change in the answers I’ve the change in the inputs:

Rate of change = 9/1 = 9

Answer:

Solution,

____________________________

Men ------------------------------ Days

_____________________________

In case of indirect proportion,

4/6= 6/X

or, 6*X= 6*4 ( cross multiplication)

or, 6x= 24

or, 6x/6= 24/6 ( dividing both sides by 6)

Hope this helps...

Good luck on your assignment..

Answer:

[tex]\boxed{4 days}[/tex]

Step-by-step explanation:

M1 = 4

D1 = 6

M2 = 6

D2 = x (we've to find this)

Since,  it is an inverse proportion (more man takes less days for the work to complete and vice versa), so we'll write it in the form of

M1 : M2 = D2 : D1

4 : 6 = x : 6

Product of Means = Product of Extremes

=> 6x = 4*6

=> 6x = 24

Dividing both sides by 6

=> x = 4 days

Answer:

Six

Step-by-step explanation:

The answer could be shown in multiple forms, but if I'm correct, the answer to this problem would be six.

=============================================================

How I got that answer:

We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.

Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.

----------

You could use the slope formula to get the job done. This is because the slope represents the rise over run

slope = rise/run

The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...

In a more written out way, the steps would be

slope = rise/run

slope = (y2-y1)/(x2-x1)

slope = (793 - 54)/(2004 - 1995)

slope = 739/9

slope = 82.111....

Answer:

[tex] Conf= 0.80[/tex]

With the confidence level we can find the significance level:

[tex]\alpha =1-0.8=0.2[/tex]

And the value for [tex]\alpha/2=0.1[/tex]. Then we can use the normal standard distribution and we can find a quantile who accumulates 0.1 of the area on each tail and we got:

[tex] z_{\alpha/2}= \pm 1.28[/tex]

Step-by-step explanation:

For this problem we have the confidence level given

[tex] Conf= 0.80[/tex]

With the confidence level we can find the significance level:

[tex]\alpha =1-0.8=0.2[/tex]

And the value for [tex]\alpha/2=0.1[/tex]. Then we can use the normal standard distribution and we can find a quantile who accumulates 0.1 of the area on each tail and we got:

[tex] z_{\alpha/2}= \pm 1.28[/tex]

Answer:

[tex]\boxed{\sf \ \ \ \text{one possibility is } f(x)=3x \ and \ g(x)=x+2 \ \ \ }[/tex]

Step-by-step explanation:

hello

h(x)=f(g(x))=3(x+2)

if we have f(x)=3x and g(x)=x+2 then

f(g(x))=f(x+2)=3(x+2)

hope this helps

Answer:

2

Step-by-step explanation:

Answer:

I hope it will help you....

Answer:

A

Step-by-step explanation:

Answer:

"But even this is admitting more than is true, for I answer roundly, that America would have flourished as much, and probably much more, had no European power had any thing to do with her."

Step-by-step explanation:

Checked 2021

Answer:

[tex]y(x)=\frac{9}{e^{1} } e^{-x} =3.310914971e^{-x}[/tex]

Step-by-step explanation:

This problem is very simple, since they give the solution for the differential equation from the start. So basically, you need to evaluate the initial conditions into the solution, and the derivative of the solution in order to find the value of the constants [tex]c_1[/tex] and [tex]c_2[/tex].

So, first of all, let's find the derivative of [tex]y(x)[/tex]:

[tex]y'(x)=c_1 e^{x} -c_2e^{-x}[/tex]

Now, let's evaluate the first initial condition:

[tex]y(-1)=c_1e^{-1} +c_2e^{-(-1)} =9\\\\c_1e^{-1} +c_2e^{1}=9\hspace{10}(1)[/tex]

Now, the second initial condition:

[tex]y'(-1)=c_1 e^{-1} -c_2e^{-(-1)}=-9\\\\c_1 e^{-1} -c_2e^{1}=-9\hspace{10}(2)[/tex]

Combining (1) and (2) we have a 2x2 System of Equations. Let's use elimination method in order to solve it:

[tex](1)+(2):\\\\c_1e^{-1} +c_2e^{1} +c_1e^{-1} -c_2e^{1}=9-9\\\\2c_1e^{-1} =0\\\\Hence\\\\c_1=0[/tex]

Replacing [tex]c_1[/tex] into (1)

[tex](0)e^{-1} +c_2e^{1}=9\\\\c_2e^{1}=9\\\\Hence\\\\c_2=\frac{9}{e^{1} } =3.310914971[/tex]

Therefore the solution of the second-order IVP is:

[tex]y(x)=\frac{9}{e^{1} } e^{-x} =3.310914971e^{-x}[/tex]

Answer:

12 boys

Step-by-step explanation:

From the above question:

Number of boys = 3

Number of girls = 2

Boys: Girls

3:2

Let :

a = boys

b = girls

Hence, a : b = 3 : 2

a/b = 3/2  

Cross Multiply

2a = 3b .......... Equation 1

a = 3b/2

If four more girls join the class, there will be the same number of boys and girls

Hence,

a: b + 4 = 3 : 3

a/b + 4 = 3/3

Cross Multiply

3a = 3(b + 4)

3a = 3b + 12 ........ Equation (2)

From Equation 1: a = 3b/2

Substitute 3b/2 for a in Equation 2 we have:

3a = 3b + 12 .........Equation 2

3(3b/2) = 3b + 12

9b/2 = 3b + 12

Cross Multiply

9b = 2(3b + 12)

9b= 6b + 24

9b - 6b = 24

3b = 24

b = 8

Substitute 8 for b in Equation 1

a = 3b/2

a = 3 × 8/2

a = 24/2

a = 12

Therefore, the number of boys in the class is 12

Answer: 136

Step-by-step explanation:

An= A1+(n-1)d

A1=16, d=8, and n=16

A16= 16 +(16-1)(8)

A16= 16(15)(8)

A16= 16+120

A16=136

Hey there! :)

Answer:

f(16) = 136 seats.

Step-by-step explanation:

This situation can be expressed as an explicit function where 'n' is the row number.

The question also states that the number of seats increases by 8. Use this in the equation:

f(n) = 16 + 8(n-1)

Solve for the number of seats in the 16th row by plugging in 16 for n:

f(16) = 16 + 8(16-1)

f(16) = 16 + 8(15)

f(16) = 16 + 120

f(16) = 136 seats.

Answer:

She can cut 122 pieces.

Step-by-step explanation:

She has 3 pieces of ribbon that are 25 yds long. In total, she has 75 yds, which is equal to 2700 in. Erika needs 22 in. pieces, so just divide 2700 by 22 to get your number.

2700/22 ≈ 122.72

Answer:

The approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 [tex]\mu_{\hat p}=0.15[/tex]

The standard deviation of this sampling distribution of sample proportion is:

 [tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]

As the sample size is large, i.e. n = 150 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.

Compute the mean and standard deviation as follows:

[tex]\mu_{\hat p}=0.15\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.15(1-0.15)}{150}}=0.0292[/tex]

So, [tex]\hat p\sim N(0.15, 0.0292^{2})[/tex]

In statistics, the 68–95–99.7 rule, also recognized as the empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the Normal distribution lie within one, two and three standard deviations of the mean, respectively.

Then,

                                  P (µ-σ < X < µ+σ) ≈ 0.68

                                  P (µ-2σ <X < µ+2σ) ≈ 0.95

                                  P (µ-3σ <X < µ+3σ) ≈ 0.997

Then the approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.

That is:

[tex]P(\mu_{\hat p}-2\sigma_{\hat p}<\hat p<\mu_{\hat p}+2\sigma_{\hat p})=0.95\\\\P(0.15-2\cdot0.0292<\hat p<0.15+2\cdot0.0292)=0.95\\\\P(0.092<\hat p<0.208)=0.95[/tex]

Hey there!

You haven't provided any answer options but here's how you would solve a problem like this.

To find the number in between two numbers, you add it up and divide it by two!

So, what's between 1 and 3? Well you do 1+3 is 4 then divide by 2 you get 2!

100 and 580? You add them to get 680 then divide by two you get 340!

In between 0.57 and 0.69? Adding gives you 1.26 and then divide by two and we have 0.63!

And with percents, let's do 45% and 67%. You add you get 112% and then divide by two you have 56%!

So, with your answer options just add them up and divide by two and see which one gives you 76%!

I hope that this helps!

Answer:

d. The length of a movie

Step-by-step explanation:

A discrete random variable is a variable which only takes on integer values.

A discrete distribution is used to describe the probability of the occurrence of each value of a discrete random variable.

From the given options, the length of a movie is not a discrete variable as it can have decimal values.

It therefore cannot have a Discrete probability distribution.

The correct option is D.

Answer:

D. A=(9)(4)

Step-by-step explanation:

area= length x width = 9x4

Answer:

2.5 mg

Step-by-step explanation:

.5 x 5 = 2.5