Calculate the surface area of the triangular prism

If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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The value of m<RQS as required to be determined in the task content is; 70°.

It follows from the task content that the measure of angle RQS is to be determined as required.

Recall, the measure of the central angle subtended by an arc is twice that which it subtends at any point on the circumference.

Therefore, m<RPS = 2 • m<RQS.

m<RQS = 140°/2

m<RQS = 70°.

Ultimately, the measure of angle RQS are; 70°.

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A box and whisker plot is a set of divided data into quartiles which is represented graphically. The quartiles are Q1,Q2,Q3. The box part represents the interquartile range that is between Q1 and Q2.

Whiskers represent the medium and maximum values that are 1.5 times the IQR below Q1 and 1.5 times of IQR above Q3. The data that comes out of the whiskers is considered individually.

The median is 14, the first quartile  Q1 is 13, the third quartile Q3 is 15, the minimum is 2 maximum is 18. IQR is 15-13=2.

To construct a data of box-and-whisker.

Draw a number line with minimum and maximum values (2-8)

Make 14 the median on the number line and draw a box from the first quartile 13 to the third quartile 15.

Draw a line from the left side of the box and another line to the right side of the box minimum and maximum 2, 18.

Plot any outliers individually.

like the below representation.

____

 |    |     |

2_131415_18

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Two lines are parallel if:

Two lines are perpendicular if:

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

Let's rewrite the given equations in the slope-intercept form:

Since:

We can conclude that the lines are parallel.

Answer:

20/3

Step-by-step explanation:

Every nth term takes the form of  a + n*d, where a is the first  term.

So 7th term = (54 = a + 7d), 13th term = (94 = a + 13d).

equate them both:

94 - 13d = 54 - 7d

40 = 6d

d = 40/6

Based on the Pythagorean theorem, in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. So, we can use this to find the possible values of the third side of the triangle.

The two given sides are 15 cm and 17 cm. We can label the unknown side as "x". Then, we can set up an equation:

15^2 + 17^2 = x^2

Simplifying this equation, we get:

225 + 289 = x^2

514 = x^2

x = sqrt(514)

Therefore, the possible value of the third side that would make it a right triangle is approximately 22.72 cm.

The range of the starting salaries is 53,000

Given,

The box and whisker plot below shows the starting salaries

The number of graduates in a small college = 120

We have to find the range of the starting salaries;

Range of a data;

The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.

Here,

Lowest value = 19,000

Highest value = 72,000

Then,

Range of the set = 72,000 - 19,000 = 53,000

That is,

The range of the given data set is 53,000

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Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Answer:

12.4 pieces of ribbon

Step-by-step explanation:

When looking in the question, we can see the term "cut into equal pieces." This can insure to us that we need to divide two numbers. Since we originally have 15.5 inches long string, and we want to cut it into strings that are 1.25 inches long. We divide :

15.5 / 1.25

==> 12.4

Tell me if it is right

Answer:

213, 123

Step-by-step explanation:

Answer:

1) 30 pounds is the weight of the bag all together

2) science book is the heaviest book

Step-by-step explanation:

bag=4 pounds

library book=2 pounds

maths book=2×4=8 pounds

science book=8×2=16 pounds

4+2+8+16=30 pounds all together

heaviest book= science book (16 pounds)

Answer:

Explanation: Function is defined as, a set that assigns x to y values, each y value associated with x has to be uniques, and there can not be two values for a single x value. Using this defination we can determine which one is a function (A to D).

(A): For x = 3 there are two values of y therefore it can not be a function.

(B): Same is true for x = 3.5, which is that there are two y values associated with the x value.

(C) Similarly, the solid dot represents a value, therefore at x = -3 there are two corresponding y values, therefore it is not a function.

(D) Each x value has a unique y value, and there aren't any two values associated with a single y value. therefore it is a Function.

The answer, therefore, is D.

Answer: The degree of 15y+v4-8 is 1

Step-by-step explanation: Hope this helps in your studies!

Answer:

The answer is 3

Step-by-step explanation:

I am sure.

Answer: i think it is 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

I am assuing it is a traingale so the tolal angle is 180

3x+52+x^2+40+70=180

3x+x^2=18

x^2+3x-18=0

(x+6)(x-3)=0

x=-6 x=3

line a x=-6; line b x=3

angle 1:

a. -6*3+52=34

b. 9+52=61

angel 2:

a. -6^2+40=76

b. 9+40=49

Angle 3: 70

a. 70+76+34=180

b. 61+49+70=180

Nana, this is the solution:

The slope intercept form is:

y = mx + b

Our equation is:

0 = -8x -6y

6y = -8x + 0

Dividing by 6 at both sides:

6y/6 = -8/6x

y = -4/3x

This is the solution.

Answer: 160

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area of a rectangle = l × w

where l is the length

w is the width

length of a rectangle is 11 yds more than twice the width is written as

l = 11 + 2w

Area = 63 yd²

(11+2w)w = 63

2w² + 11w - 63 = 0

Solve the quadratic equation

( w + 9) ( 2x - 7) = 0

w = - 9 w = 7/2 or 3.5

Since width is always positive w is 3.5 yd

l = 11 + 2(3.5)

l = 11 + 7

l = 18 yd

The length is 18 yd

The length is 18 ydThe width is 3.5 yd

Hope this helps you

Answer:

Has this question in gr 8 struggled with it couldnt figure it out and people on brainy dont help either

u diviide the number of candies by the number of people

Step-by-step explanation:

5/4

Answer:

Each child would get 1 1/4 of a candy bar

Step-by-step explanation:

If Seymour is 1 out of 4 kids and has 5 candy bars each kid gets 1 candy bar (4 candy bars) and then there is 1 candy bar remaining. This 1 candy bar can then be split into 1/4ths so each kid gets 1 1/4 candy bars.

Answer:

V=whl=2·2.5·4=20

Step-by-step explanation:

Answer:

2880 feet³

Step-by-step explanation:

since the question is asking for cubic feet we know we're finding volume.

v=l·w·b

v=4·24·30

=2880

The equation of the line k parallel to line j and passes through (-4, 4) is

y = - 9 / 7 x - 8 / 7

Equation of a line can be represented as follows:

y = mx + b

where

Therefore, the line k is parallel to the line j, y =  - 9 / 7 x + 10 / 7  and passes through (-4, 4),

Parallel lines have the same slope.

Hence, let's find the y-intercept of the equation k using (-4, 4)

4 = - 9 / 7 (-4) + b

4 - 36 / 7 = b

b = - 8 / 7

Therefore,

the equation is y = - 9 / 7 x - 8 / 7

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Answer:

the answer is 27

i did this by doing 6 x 2 which is 12 so i then did 16 - 12 which is 4 then i add the 2 in it which is 42 i then did 6 x 7 which is 42 and thats 0

this is my statement and i did this on paper and got this right!

Answer:

27

Step-by-step explanation:

See photo below

Answer:

it's c

Step-by-step explanation:

when doing expression the x means a unknown number and c doesn't have a number so it's C

Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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Answer:

15-739-28

Step-by-step explanation:

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.