find the total area of the prism

Answer:

The lengths of the sides are 20 cm and 20 cm

Step-by-step explanation:

Given

Perimeter, P = 80cm

Represent the length and width with L and W, respectively;

[tex]P= 2*(L + B)[/tex]

Substitute 80 for P

[tex]80 = 2 * (L + B)[/tex]

Divide through by 2

[tex]40 = L + B[/tex]

[tex]L + B = 40[/tex]

Make L the subject of formula

[tex]L = 40 - B[/tex]

Area of a rectangle is calculated as thus;

[tex]Area = L * B[/tex]

Substitute 40 - B for L

[tex]Area = (40 - B) * B[/tex]

Express this as a function

[tex]A(B) = (40 - B)* B[/tex]

[tex](40 - B)* B = A(B)[/tex]

Set A(B) = 0 to determine the roots

Hence;

[tex](40 - B)* B = 0[/tex]

[tex]40 - B = 0[/tex] or [tex]B = 0[/tex]

[tex]40 = B[/tex] or [tex]B = 0[/tex]

[tex]B = 40[/tex] or [tex]B = 0[/tex]

The maximum area of a rectangle occurs at half the sum of the roots;

So;

[tex]B= \frac{B_1 + B_2}{2}[/tex]

[tex]B= \frac{40+0}{2}[/tex]

[tex]B= \frac{40}{2}[/tex]

[tex]B = 20[/tex]

Recall that [tex]L = 40 - B[/tex]

[tex]L = 40 - 20[/tex]

[tex]L = 20[/tex]

Hence the lengths of the sides are 20 cm and 20 cm

Answer:

The least possible price is  p  =  £110

Step-by-step explanation:

From the question we are told that

     The number of bracelets to be made is  [tex]n = 150[/tex]

      The length of silver require for on bracelet is  [tex]x = 26 \ cm = 0.26 \ m[/tex]

      The option of silver length packs that she buys is  a =  10.5 m  packs

                                                                                           b  =  3.7 m packs

    Generally

                   1 bracelet   [tex]\to[/tex]  0.26 m  

                   150 bracelet [tex]\to[/tex]  z

=>        [tex]z = \frac{150 * 0.26}{1}[/tex]

=>        [tex]z = 39 \ m[/tex]

Now for option a  i.e  10.5 m  per pack

    The number of packs require is

        [tex]v = \frac{z}{a}[/tex]

=>     [tex]v = \frac{39}{ 10.5}[/tex]

=>      [tex]v = 3.7 1[/tex]

given that the number of packs cannot be a fraction but an integer hence she needs to purchase v =  4

and that 4 packs would equal  t  =  4 * 10.5 =  42 meters of  silver

 Now for option d  i.e  3.7 meters per pack  

 The number of packs requires is  

           [tex]w = \frac{z}{b}[/tex]

=>        [tex]w = \frac{39}{3.7}[/tex]

=>        [tex]w = 10.54[/tex]

given that the number of packs cannot be a fraction but an integer hence she needs to purchase w= 11

and that 11 packs would equal  t  = 11 * 3.7 =  40.7 meters of  silver

So the comparing the option and option b we see that for her to pay as little as possible she needs to go for option b since option be will produce the 150  bracelet with a little excess while option a will produce the 150 bracelet with much excess

    Assuming the price for the 3.7 m  pack is    £10

     And the price for the 10.7 pack is  £30

The least possible amount she would pay is  

                 [tex]p = 10 * 11[/tex]

                 p  =  £110  

Answer:

A. A data set is a collection of similar data.

D. A data set contains data all of which have some common characteristic.

Answer:

a.

[tex]\mathbf{r_1 = (t,0) \implies t = 0 \ to \ 1}[/tex]

[tex]\mathbf{r_2 = (2-t,t-1) \implies t = 1 \ to \ 2}[/tex]

[tex]\mathbf{r_3 = (0,3-t) \implies t = 2 \ to \ 3}[/tex]

b.

[tex]\mathbf{\int \limits _{c} F \ dr =\dfrac{11 \sqrt{2}+11}{6}}[/tex]

Step-by-step explanation:

Given that:

C: counterclockwise around the triangle with vertices (0, 0), (1, 0), and (0, 1), starting at (0, 0)

a. Find a piecewise smooth parametrization of the path C.

r(t) = { 0

If C: counterclockwise around the triangle with vertices (0, 0), (1, 0), and (0, 1),

Then:

[tex]C_1 = (0,0) \\ \\ C_2 = (1,0) \\ \\ C_3 = (0,1)[/tex]

Also:

[tex]\mathtt{r_1 = (0,0) + t(1,0) = (t,0) }[/tex]

[tex]\mathbf{r_1 = (t,0) \implies t = 0 \ to \ 1}[/tex]

[tex]\mathtt{r_2 = (1,0) + t(-1,1) = (1- t,t) }[/tex]

[tex]\mathbf{r_2 = (2-t,t-1) \implies t = 1 \ to \ 2}[/tex]

[tex]\mathtt{r_3 = (0,1) + t(0,-1) = (0,1-t) }[/tex]

[tex]\mathbf{r_3 = (0,3-t) \implies t = 2 \ to \ 3}[/tex]

b Evaluate :

Integral of (x+2y^1/2)ds

[tex]\mathtt{\int \limits ^1_{c1} (x+ 2 \sqrt{y}) ds = \int \limits ^1_{0} \ (t + 0) \sqrt{1} } \\ \\ \mathtt{ \int \limits ^1_{c1} (x+ 2 \sqrt{y}) ds = \begin {pmatrix} \dfrac{t^2}{2} \end {pmatrix} }^1_0 \\ \\ \mathtt{\int \limits ^1_{c1} (x+ 2 \sqrt{y}) ds = \dfrac{1}{2}}[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \int \limits (x+2 \sqrt{y} \sqrt{(\dfrac{dx}{dt})^2 + (\dfrac{dy}{dt})^2 \ dt } }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \int \limits 2- t + 2\sqrt{t-1} \ \sqrt{1+1} }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} \int \limits^2_1 2- t + 2\sqrt{t-1} \ dt }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} } \ \begin {pmatrix} 2t - \dfrac{t^2}{2}+ \dfrac{2(t-1)^{3/2}}{3} (2) \end {pmatrix} ^2_1}[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} } \ \begin {pmatrix} 2 -\dfrac{1}{2} (4-1)+\dfrac{4}{3} (1)^{3/2} -0 \end {pmatrix} }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} } \ \begin {pmatrix} 2 -\dfrac{3}{2} + \dfrac{4}{3} \end {pmatrix} }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} } \ \begin {pmatrix} \dfrac{12-9+8}{6} \end {pmatrix} }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} } \ \begin {pmatrix} \dfrac{11}{6} \end {pmatrix} }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \dfrac{ \sqrt{2} }{6} \ (11 )}[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \dfrac{ 11 \sqrt{2} }{6}}[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = \int \limits ^3_2 0+2 \sqrt{3-t} \ \sqrt{0+1} }[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = \int \limits ^3_2 2 \sqrt{3-t} \ dt}[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = \int \limits^3_2 \begin {pmatrix} \dfrac{-2(3-t)^{3/2}}{3} (2) \end {pmatrix}^3_2 }[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = -\dfrac{4}{3} [(0)-(1)]}[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = -\dfrac{4}{3} [-(1)]}[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = \dfrac{4}{3}}[/tex]

[tex]\mathtt{\int \limits _{c} F \ dr =\dfrac{11 \sqrt{2}}{6}+\dfrac{1}{2}+ \dfrac{4}{3}}[/tex]

[tex]\mathtt{\int \limits _{c} F \ dr =\dfrac{11 \sqrt{2}+3+8}{6}}[/tex]

[tex]\mathbf{\int \limits _{c} F \ dr =\dfrac{11 \sqrt{2}+11}{6}}[/tex]

Step-by-step explanation:

utilise the formula a+(n-1)d

a is the first number while d is common difference

Answer:

22

Step-by-step explanation:

Using the formular, Un = a + (n - 1)d

Where n = 10; a = -23; d = 5

U10 = -23 + (9)* 5

U10 = -23 + 45 = 22

Answer:

C) Local Eats

Step-by-step explanation:

So this one is pretty simple in retrospect. Just some proportions

Food Queen) 3.60:6=.60:1        1 pound is 60 cents

Grocery Smart) $1/4:1/2= $1/2:1   $1/2=50 cents       1 pound is 50 cents

Fresh Farm) $3:4=$1.50:2=.75:1       1 pound is 75 cents

Local Eats) .49:1     1 pound is 49 cents

As you can see, the answer is C) Local Eats

Step 1:

First, let's convert all of the numbers on the numerator side to decimals. Food Queen, Fresh Farm, and Local Eats are already in decimals, but Grocery Smart is not. 1/4 is 25%, which is equal to 0.25.

Step 2:

We need to convert all the values to represent the price of one pound. To do that, we just divide as written.

Food Queen: 3.00 ÷ 6 = 0.50

Grocery Smart: 0.25 ÷ 0.5 = 0.50

Fresh Farm: 3.00 ÷ 4 = 0.75

Local Eats: 0.49

Our answer: C. Local Eats. $0.49

Answer:

Drag the ruler over each side of the triangle to find its length.

The length of AB is

✔ 5

.

The length of BC is

✔ 4

.

Drag the protractor over each angle to find its measure.

The measure of angle C is

✔ 90°

.

The measure of angle B is

✔ 36.9°

.

Step-by-step explanation:

The length of sides AB and BC of the triangle will be 5 units and 4 units. And the measure of angle C and angle B of the triangle will be 90° and 37°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Drag the ruler over each side of the triangle to find its length.

The length of side AB of the triangle is 5 units.

The length of side BC of the triangle is 4 units.

Drag the protractor over each angle to find its measure.

The measure of angle C of the triangle is 90°.

The measure of angle B of the triangle is 37°.

The length of sides AB and BC of the triangle will be 5 units and 4 units.

And the measure of angle C and angle B of the triangle will be 90° and 37°.

More about the right-angle triangle link is given below.

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Answer:

A. 385.56 square meters.

B. 142.56 square meters.

Step-by-step explanation:

A house 27m by 9m is surrounded by a walkway 1.8m wide.

a) Find the area of the region covered by the house and the walkway.

​b) Find the area of the walkway.

Let

Length of the house=l=27m

Width of the house=w=9m

Wideness of the walkway=x=1.8m

Area of the region covered by the house and the walkway

=( L + 2*x) * (w + 2*x)

= (27+2*1.8)*(9+2*1.8)

=(27+3.6)*(9+3.6)

=(30.6)*(12.6)

=385.56 square meters.

​b) Area of the walkway

= (L + 2*x)*(w + 2*x) - l*w

= (27+2*1.8)*(9+2*1.8) - 27*9

=(27+3.6)*(9+3.6) - 243

=(30.6)*(12.6) - 243

=385.56 - 243

=142.56 square meters.

Answer:

A) 0.12. Yes. Choosing a green and blue M&M is possible

B) 0.43. Yes. Choosing a yellow and red M&M is possible

C) 0.78

Step-by-step explanation:

First of all, the summation of the distribution of all colours is;

Σ(all colors ) = 22% + 20% + 23% + 10% + 6% + 6% + 13% = 100%, or 1.

Thus;

a) P(green candy or blue candy) is;

P(GREEN ∪ BLUE) = P(G) + P(BL)

P(GREEN ∪ BLUE) = 6%+6%

P(GREEN ∪ BLUE) = 12% or 0.12

Now, due to the fact that we have to choose ONE candy and only ONE candy at random, then they are mutually exclusive: Yes. Choosing a green and blue M&M is possible

b)P(yellow candy or red candy is;

P(YELLOW ∪ RED) = P(Y) + P(R)

P(YELLOW ∪ RED) = 20% + 23% = 43% or 0.43

Yes. Choosing a yellow and red M&M is possible

c) P(NOT PURPLE)

the probability of having a purple is;

P(PURPLE) = 22% or 0.22

So, the Probability of NOT having a PURPLE is 1 - 0.22 = 0.78

Answer:

The fraction that represents the heart in the diagram shown is 7/3

Step-by-step explanation:

For this problem, we have to find the fraction expressed by the number line in the diagram shown.

First off, we know that the fraction will be between 2 and 3. Second, we know that each little dash between 2 and 3 represents 1/6.So, let's use this information to find the fraction.

Since the heart is two dashes away from 2, then this part of the fraction is 2/6 which can also be simplified to 1/3.

2 1/3

Since we can not have a mixed fraction, then we are going to turn this mixed number into an improper fraction. We do this by multiplying 2 with the denominator (which is 3) and adding the numerator (which is 1) to that product. Our denominator will stay the same in the final fraction.

2 1/3 = 7/3

So, the fraction represented by the heart is 7/3

Answer:

16/7

Step-by-step explanation:

There are 7 divisions between the numbers 2 and 3

So the denominator is 7

The heart is at the second mark

We are past the 2 mark so it is

2 2/7

Changing this from a mixed number to an improper fraction

(7*2+2) /7

16/7

y represents the range for an ordered pair (x, y). Option A is correct.

For an ordered pair (x, y), What y represents is to determine.

Range of the function is the output value of the function.

Here, in ordered pair (x, y) x represents the values of independent variable terms as domain. And for every value of x their is exist or output values y this  set of y values is called as range.

Thus, y represents the range for an ordered pair (x, y).

Learn more about range here:

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Answer:

The 3 years investment earns more interest

Step-by-step explanation:

Given

Principal, P = $5,000

Required

Determine which earns more interest

When Rate = 1.75% and Year = 2

Interest is as follows;

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

Substitute 1.75 for R, 5000 for P and 2 for T

[tex]I = \frac{5000 * 1.75 * 2}{100}[/tex]

[tex]I = \frac{17500}{100}[/tex]

[tex]I = \$175[/tex]

When Rate = 1.25% and Year = 3

Interest is as follows;

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

Substitute 1.25 for R, 5000 for P and 3 for T

[tex]I = \frac{5000 * 1.25 * 3}{100}[/tex]

[tex]I = \frac{18750}{100}[/tex]

[tex]I = \$187.5[/tex]

Comparing the interest of both investments, the 3 years investment earns more interest

Answer:

7

Step-by-step explanation:

it's simply 13 - 6

7 it the answer, that was easy

Answer:

17/16 OR [tex]1\frac{1}{16}[/tex] minutes

Step-by-step explanation:

Since Jayla spent 1/16 of a minute AND one whole minute watching a millipede crawl, we'd need to first add the two numbers.

Since the given minute is out of 16, we can convert the one minute to 16/16.  This means we can add the other 1/16 of a minute.

This leaves us with Jayla watching the millipede for 17/16 OR [tex]1\frac{1}{16}[/tex] minutes.

Hope this helps!! <3 :)

Answer:

choice 1,2,4,5 from top to bottom

Step-by-step explanation:

1:the points given are in the line where both planes intersect

2:point H is not on any plane

3:in the diagram point F is on plane R so false

4:if you connect the points given they will intersect so not collinear

5:the points F and G are on the plane R

6:so F is on plane R but H is not on any do false

Answer:

1

Step-by-step explanation:

Answer:

Hello There!!

Step-by-step explanation:

The answer is 1 as that means its certain that the event will happen.

hope thus helps,have a great day!!

~Pinky~

Answer:

$0.75

Step-by-step explanation:

Given that

Number of bags of popcorn bought = 4

Total money spent = $3.00

To find:

Unit rate per bag of popcorn = ?

i.e. price of one bag of popcorn is to be find out.

Solution:

We can use ratio here to find the rate of one bag of popcorn.

4 bags bought at $3

4 bags : $3

Let us divide both the sides with 4.

[tex]\frac{4}4[/tex] bags : $ [tex]\frac{3}4[/tex]

OR

1 bag bought at $ 0.75

We can alternatively use unitary method.

4 bags are bought at $ 3

1 bag is bought at $ [tex]\frac{3}{4}[/tex]

1 bag is bought at $0.75.

So, unit rate per bag of popcorn is $0.75.

Answer:

The probability that the diagnosis is correct is 0.95249.

Step-by-step explanation:

We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.

Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.

Let the probability that people in the United States have diabetes = P(D) = 0.083.

So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917

Also, let A = event that the diagnostic test is accurate

So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98

And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95

Now, the probability that the diagnosis is correct is given by;

    Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')

                      = (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)

                      = 0.08134 + 0.87115

                      = 0.95249

Hence, the probability that the diagnosis is correct is 0.95249.

Answer: the opposite of 15

Step-by-step explanation:

Every number 'a' on number line is exactly opposite of '-a'.

So, 15 is the opposite of '-15'

Also absolute value for any number gives its positive value, soabsolute value of 15 = 15

Moving 0 to 15 gives the  distance between zero and 15.

So all statements are true except "the opposite of 15".

Hence, the required statement is "the opposite of 15".

Answer:

the approximate area of this circle is 200.96 inches long.

Step-by-step explanation:

To answer this problem we need to remember that the area of a circle is given by the formula:

Area = π[tex]r^2[/tex] where r is the radius.

and the perimeter is:

Perimeter = 2πr

Now, the problem tells us that the circle is enclosed by a piece of rope that's 50.24 inches long. So the perimeter of the circle is 50.24 inches.

Since we have the value of the perimeter and the value of pi, we are going to substitute these values in the perimeter formula to find r.

Perimeter = 2πr

50.24=2(3.14)r

50.24= 6.28r

50.24/6.28= r

8= r

Thus, the radius of the circle is 8 inches long.

Now, we can use this value to find the area of the circle:

Area = π[tex]r^2[/tex]

Area = π[tex]8^2[/tex]

Area = 3.14 (64)

Area = 200.96

Therefore, the approximate area of this circle is 200.96 inches long.

The approximate area of a circle enclosed by a piece of rope is 200.96 square inch.

The length of rope by which a circle is made, is known as circumference of circle.

Circumference of circle =  [tex]2\pi r[/tex]   , where r is radius of circle.

Since, length of rope is 50.24 inches.

                [tex]2\pi r=50.24\\\\r=\frac{50.24}{2*3.14}=8 inch[/tex]

Area of circle = [tex]\pi r^{2}[/tex]

                      = [tex]3.14 *(8)^{2}=200.96[/tex] square inch

Thus,  the approximate area of a circle enclosed by a piece of rope is 200.96 square inch.

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Answer: [tex]4x^2-21x-2[/tex] .

Step-by-step explanation:

Given: The difference of two trinomials is [tex]x^2 -10x + 2[/tex]. If one of the trinomials is [tex]3x^2 - 11x - 4[/tex].

Then, the other trinomial will be ([tex]3x^2 - 11x - 4[/tex] ) + ([tex]x^2 -10x + 2[/tex])

[tex]=3x^2-11x-4+x^2-10x+2\\\\=3x^2+x^2-11x-10x-4+2\\\\=4x^2-21x-2[/tex]

Hence, the other trinomial could be : [tex]4x^2-21x-2[/tex] .

Answer:

C. Graph C

Step-by-step explanation:

In a scatter plot, a positive correlation coefficient suggests that as one variable increases the other increases as well, or as one decreases, the other decreases.

Also, the more clustered the data points are along the line of best fit, the higher the value of the coefficient, whether positive or negative.

Graph C shows a positive correlation because as the variable on the x-axis increases, the variable on the y-axis also increases. The data points are more clustered along the line if best fit, if we draw one. This suggest a positive correlation coefficient (r) as strong as 0.75.

Graph C has a correlation coefficient, r, that is closer to 0.75.

Answer: graph A ‼️

Step-by-step explanation:

The given equation is in the form ax^2+bx+c = 0 with

D = discriminant

D = b^2 - 4ac

D = 4^2 - 4(2)(1-3m)

D = 16 - 8(1-3m)

D = 16 - 8 + 24m

D = 24m + 8

D > 0

24m + 8 > 0

24m > -8

m > -8/24

m > -1/3

As long as m is larger than -1/3, then the discriminant is positive. There are infinitely many solutions to pick from.

Answer:

[tex]x = 3.6[/tex]

Step-by-step explanation:

To find the area of a rectangle, you multiply its length by its width. The formula is [tex]lw = a[/tex].

We already know the length, 5, and the area, 18, so we can plug it into the equation.

[tex]5\cdot w=18[/tex]

We can simplify this equation by dividing both sides by 5.

[tex]5\cdot w \div5 = 18\div5\\\\w = 3.6[/tex]

Hope this helped!

Answer: x= 13

Step-by-step explanation:

Answer:

Hey there!

We can write the equation:

0.65x=39

x=60

The dress originally sold for 60 dollars.

Hope this helps :)

Answer:

Reject the null hypothesis because the value of null is outside the interval.

Step-by-step explanation:

Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case p-value is less than critical value then we should reject the null hypothesis.

Answer:

D no mistakes

Step-by-step explanation:

3+(-4)-7 is equal to 3-4-7=-8

Answer:0

Step-by-step explanation:

3+(-4)-7 when there are parenthesis around a negative number you flip it to positive and then 4+3-7=0

Answer:

Maximum at (-6,51), or value of f(-6) = 51

Step-by-step explanation:

f(x) = 8*log(x+7)-8*x+3

differentiate with respect to x

f'(x) = 8/(x+7) -8

To find maximum, set f'(x) = 0

f'(x) = 8/(x+7) -8 = 0

solver for x

x= -6

evaluate f(x) at x=-6

f(-6) = 8log(-6+7) - 8(-6) + 3

= 0 +48 +3

= 51

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