8. Mrs. Reyes has 4 mangoes, 5 guavas, and 2 bananas in her basket. What is the probability that one can pick a guava?
A. 2 out of 11 or 2/11
B. 5 out of 11 or 5/11
C. 4 out of 11 or 4/11

9. What is the probability of choosing a blue paper if there are 3 red papers and 4 blue papers in the box?
A. 4 out of 7 or 4/7
B. 3 out of 7 or 3/7
C. 0 out of 7 or zero probability

10. In the numbers 2,2,2,5,5,2,3 What is the probability of getting 2?
A. 2/7
B. 3/7
C. 4/7​

The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).

Sequences are sets of elements characterized by at least a rule. In this case, the sequence shown is characterized by a function that generates even numbers equal or greater than 10. The function behind the sequence is shown below:

s = 10 + 2 · (n - 1)     (1)

Where n is the element index.

The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).

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The time taken by the rock will be 8.77 seconds.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

Given that:-

The equation for free fall at the surface of some planet (s in meters, t in seconds) is s = 2.86t²

The time will be calculated by using the speed formula.

Speed = Distance \ Time

25.1   = 2.86t² \ t

t   =  25.1 / 2.86

t   =  8.77 seconds

Therefore the time taken by the rock will be 8.77 seconds.

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Answer: C

Step-by-step explanation:

[tex]a^{b} \times a^{c}=a^{b+c}[/tex], so [tex]4^{-5} \times 4^{8}=4^{-5+8}=4^{3}[/tex].

The only option that is equal to this is C

Answer: [tex]5x^{2}-4[/tex]

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)=4x^{2}+1+x^{2}-5=\boxed{5x^{2}-4}[/tex]

Answer: 14 - 5i

Step-by-step explanation:

Answer:

-10i+15 or 15-10i

Step-by-step explanation:

Use the cross multiply method

(4+1)(3-2i)

4x3=12

4x-2i=-8i

1x3=3

1x(-2i)=-2i

now we sum our similarities.

-10i+15

Answer:

$14.4

Step-by-step explanation:

there are 2 adults so 2 children will get the discount

4.50 + 4.50 + 1.375 + 1.375 + 2.75 = $14.5

Answer:

Step-by-step explanation:

Answer:

f(x) = -3x + 5

Step-by-step explanation:

The slope of the function is -3 as the outputs decrease by three for each iteration.

The constant is 5 and can be determined if you plug in 1 as an x value and solve for c in an equation like this: -3(1) + c = 2

Answer:

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

Explanation:

Let's solve for y to get the equation into y = mx+b form, aka slope intercept form.

4x-8y= -6

-8y= -6-4x

y = (-6-4x)/(-8)

y = -6/(-8) + (-4x)/(-8)

y = 3/4 + (1/2)x

y = (1/2)x + 3/4

This is now in y = mx+b form

m = 1/2 = slope

b = 3/4 = y intercept

We'll ignore the y intercept and focus on the slope only.

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

Rule: If the slope of a line is a/b, then the perpendicular slope is -b/a

Flip the fraction and flip the sign.

In this case, the original slope 1/2 has a perpendicular slope of -2/1 or simply -2.

The original slope multiplied with the perpendicular slope yields -1. So (1/2)*(-2/1) = -1

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

Another rule: Two parallel lines always have equal slopes, but different y intercepts.

The original slope is 1/2, so the parallel slope is also 1/2.

Answer:

∠ 4 = 80°

Step-by-step explanation:

∠ 5 and 100° are vertical angles and are congruent , so

∠ 5 = 100°

∠ 4 and ∠ 5 are same- side interior angles and sum to 180° , that is

∠ 4 + ∠ 5 = 180°

∠ 4 + 100° = 180° ( subtract 100° from both sides )

∠ 4 = 80°

Answer: He must have atleast 98 points on the next exam in order to get an average of 92 points.

Step-by-step explanation: To calculate average, you need to add all the numbers given, and divide the sum by how many numbers there are. 87 + 89 + 94 + 98 (equals 368), and divide 368 by 4. You will get the average of 92 as its result.

The length of the actual tree will be 72 inches.

Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.

The equation whose highest degree of the variable is 1 is called a linear equation.

Here given that the length of a painting of the tree is 2/9 of the actual length of the tree.

So mathematically the length of a painting= (2/9)*the length of actual tree

Let the length of the actual tree is x

then from above it is clear that the length of a painting of the tree= (2/9)x

Given the length of the painting is 16 inches.

So the linear equation will be (2/9)x= 16

⇒ x= 16/(2/9)

⇒x= 16*9/2

⇒x=72 inches

Therefore the length of the actual tree will be 72 inches.

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The value of x, y and z will be 1, 5 and 2 respectively

An augmented matrix in linear algebra is a matrix created by joining the columns of two supplied matrices, often so that the same basic row operations may be applied to each of the given matrices individually.

Lets write the augmented matrix by writing the coefficients of all the variables:

3      -4    -5      -27              Row 1

5        2     -2      11               Row 2

5       -4      4      -7               Row 3

We need to get

1   0   0

0   1    0

0   0   1

then the values of x, y, and z will be in the last column.

The row operation (R1=R1/3) is used to get the identity matrix.

1      -4/3    -5/3      -9              Row 1

5        2        -2      11               Row 2

5       -4        4      -7               Row 3

Add row 2 to row 1 and multiply by 5 (R2=R2(5)R1).

1      -4/3      -5/3      -9              Row 1

0     26/3      19/3     56              Row 2

5       -4             4      -7               Row 3

Add row 3 to row 1 and multiply by 5 (R3=R3(5)R1).

1      -4/3      -5/3      -9              Row 1

0     26/3      19/3     56              Row 2

0      8/3       37/3    38               Row 3

Multiply row 2 by 326 (R2=(3/26)R2)

1      -4/3      -5/3        -9              Row 1

0     1       19/26    84/13              Row 2

0      8/3       37/3    38               Row 3

Add row 2 multiplied by 4/3 to row 1 (R1=R1+(4/3)R2)

1      0        -9/13     -5/13              Row 1

0     1       19/26    84/13              Row 2

0      8/3       37/3    38               Row 3

Add row 3 to row 2 and multiply the result by 8/3 (R3=R3(8/3)R2).

1      0        -9/13     -5/13              Row 1

0     1       19/26    84/13              Row 2

0    0       135/13    270/13           Row 3

Multiply row 3 by 13/135 (R3=(13/135)R3)

1      0        -9/13     -5/13              Row 1

0     1       19/26    84/13              Row 2

0    0          1         2                    Row 3

Add row 3 multiplied by 9/13 to row 1 (R1=R1+(9/13)R3)

1      0       0            1                  Row 1

0     1       19/26    84/13              Row 2

0    0          1         2                    Row 3

Row 2 is reduced by row 3 multiplied by 19/26 (R2=R2(19/26)R3).

1      0       0            1                  Row 1

0     1          0          5                 Row 2

0    0          1         2                    Row 3

Hence the value of x, y and z will be 1, 5 and 2 respectively

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Answer:

Median is 6

standard deviation is 2.39

Step-by-step explanation:

the median is the mid number in the data set

The median formula is {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number.

There are 51 data points in this set (n = 51)

so 51 / 2 = 25.5, the. number in the 25th slot is our median

3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11

the standard deviation is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

If we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.

The foreign exchange market works according to the principles of firms, households, and investors:

Therefore, if we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.

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Answer:

The lengths of HJ and JK are 50 and 72 respectively.

Given:

J is between H and K.

HJ=2x+4

JK=3x+3

HK=22

Step-by-step explanation:

The total length is given as:

HJ+JK=HK

⇒ (2x+4)+(3x+3)=22

⇒ 5x+7=22

⇒ 5x=22-7

⇒ 5x=15

⇒ x=3

Thus, the length of HJ is (2x+4)=(2*3+4)=10

And the length of JK is (3x+3)=(3*3+3)=12

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The lengths of HJ and JK are 50 and 72 respectively.

Given: J is between H and K. the length of HJ=2x+4, JK=3x+3, and HK=22.

The line HJ and JK are  collinear then the total length is given as: HJ+JK=HK

substitute values

⇒ (2x+4)+(3x+3)=22

⇒ 5x+7=22

⇒ 5x=22-7

⇒ 5x=15

⇒ x=3

Thus, the length of HJ is (2x+4)=(2*3+4)=10

And the length of JK is (3x+3)=(3*3+3)=12

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Answer:

B

Step-by-step explanation:

= (7x+1) • (8x)

= 56x^2 + 8x

The value of B1 shows a fall in demand as price rises by a unit. The point prediction is given as y = 306,560.8

The regression equation shows that y= 306,619-27.71.x

b1 = -27.71

The interpretation for b1 is that if the price of this good is increased by 1, then the demand for the good would fall by about 27.71.

The regression line equation is given as

y= 306,619-27.71.x

when x which is price is = 2.10

Then the value of y would be:

y = 306,619 - 27.71*2.10

y = 306,560.8

c. a 95% C1 for B1 is given as:

1.96 * 27.71.

= 54.31

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Using the z-distribution, the minimum sample size required by this student is of 385.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

We want a margin of error of M = 0.05, with no prior estimate, hence [tex]\pi = 0.5[/tex], then we have to solve for n to find the minimum sample size.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96(0.5)[/tex]

[tex]\sqrt{n} = 1.96 \times 10[/tex]

[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]

n = 384.16

Rounding up, the minimum sample size is of 385.

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The correct answer are as follows:

A. False

B. True

C. False

D. False

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

A. Since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

False, it is the y-intercept of the function that indicates the amount at the start of the experiment.

B. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

True, the y-intercept is given when x = 0, indicating the initial value of the function.

C. Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.

False, because the maximum value of each table is given in different times, and also the initial value of each table is different.

D. Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.

False, the growth rate is not given by the initial value. If we model both tables with an exponential function, the count of bacteria A quadruped in two days, and the count of bacteria B doubled in one day, so they have the same growth rate.

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Answer:

Step-by-step explanation:

The answer to this problem can be found by writing an equation for the total interest in terms of the amounts invested at each rate.

__

Let x represent the amount invested at 9% (the higher rate). Then (11000-x) is the amount invested at 3%, and the total interest earned is ...

  0.09x +0.03(11000 -x) = 750

  0.06x = 420 . . . . . . . subtract 330 and simplify

  x = 7000 . . . . . . . divide by 0.06 . . . amount invested at 9%

  11000 -7000 = 4000 . . . amount invested at 3%

Larry invested $4000 at 3%, and $7000 at 9%.

_____

Additional comment

In "mixture" problems of this type, it generally works well to let the variable represent the amount of the highest-value contributor. That way, the equations end up with positive coefficients, tending to reduce errors.

Answer:

[tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}[/tex]

The sigma notation means to find the sum of the given geometric series where the first term is when n = 1 and the last term is when n = ∞.

To find the first term in the series, substitute n = 1 into the expression:

[tex]\implies a_1=4^{-1}=\dfrac{1}{4}[/tex]

The common ratio of the geometric series can be found by dividing one term by the previous term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{4^{-2}}{4^{-1}}=\dfrac{1}{4}[/tex]

As | r | <  1  the series is convergent.

When a series is convergent, we can find its sum to infinity (the limit of the series).

Sum to infinity formula:

[tex]S_{\infty}=\dfrac{a}{1-r}[/tex]

where:

Substitute the found values of a and r into the formula:

[tex]S_{\infty}=\dfrac{\frac{1}{4}}{1-\frac{1}{4}}=\dfrac{1}{3}[/tex]

Therefore:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}=\dfrac{1}{3}[/tex]

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Answer:

21, 8

Step-by-step explanation:

The second endpoint is of the form (X, 8) since it's parallel to the x axis.

Given the congruence of the two segments, we can tell that its length is 16 units (since [tex]|4-20| = |-16|= 16[/tex])

At this point the two possible endpoints for the segment are [tex](5-16; 8)[/tex] or [tex](5+16, 8)[/tex]. The fact that the segment has to sit in the first quadrant rules out the first option (it's endpoint will be at (-11, 8) which will set most of it in the second quadrant) and we're left with (21, 8)

The value of DG is 4x + 45

From the question, we are to determine the value of DG

From the given information,

DE = 2x + 17

EF = 8

FG = 2x + 20

Then,

DG = DE + EF + FG

DG = 2x + 17 + 8 + 2x + 20

DG = 4x + 45

Hence, the value of DG is 4x + 45

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To solve this problem, you will need to know the formula to find the circumference of a circle given the diameter of a circle. After calculating the circumference, you will then divide this result by 5 to obtain the final answer needed for this problem.

The circumference of a circle is found using the formula C = 2πr.

[tex]C = 2\pi r[/tex]

We are given the diameter. The radius can be found using r = D/2.

[tex]\displaystyle r=\frac{D}{2}[/tex]

[tex]\displaystyle r=\frac{14}{2}[/tex]

[tex]r=7[/tex]

Plug in the radius to the formula for a circle's circumference: C = 2πr.

[tex]C = 2 \pi (7)[/tex]

Rearrange the equation to distribute the 7 into the 2π.

[tex]C = 7(2\pi)[/tex]

Distribute the 7.

[tex]C=14\pi[/tex]

To find one-fifth of the distance (formally termed the circumference) around the circle, divide the circumference by 5.

[tex]\displaystyle \frac{14\pi}{5}[/tex]

If you are looking for a simplified answer in terms of π, this will suffice. If you need an exact answer that does not reference π, continue reading.

For a solution not in terms of π, first, multiply 14 by π.

[tex]14\times\pi = 43.98229715[/tex]

Divide this value by 5.

[tex]\displaystyle \frac{43.98229715}{5} = 8.7964594[/tex]

To make this easier to present, round to the hundredths place.

[tex]8.7964594 \approx 8.80[/tex]

The final answer, dependent on the value you are asked to provide, is:

[tex]{\boxed{\displaystyle \frac{14\pi}{5} \ \text{inches}}[/tex]

[tex]\boxed{\text{approximately} \ 8.8 \ \text{inches}}[/tex]

Answer: I don’t understand

Step-by-step explanation:

Answer:

Step-by-step explanation:

A function is defined so that for each input, there is no more than one output.