A five-question quiz is taken in which the first and second questions have four answer choices, the third and fourth questions have three answer choices, and the last question has five answer choices. If a student randomly marks an answer for each question, what is the expected number of questions he will answer correctly?

Answer:

5 calories.

Step-by-step explanation:

We begin by calculating the rate at which Raquel burns calories while hiking.

This can be obtained as follow:

Calories burned = 225 calories

Time = 45 mins

Rate =?

In this case, the Rate is simply defined as calories per unit time. Mathematically, it is expressed as:

Rate = Calorie/time

With the above formula, we can obtain the rate at which Raquel burns calories as follow:

Calories burned = 225 calories

Time = 45 mins

Rate =?

Rate = Calorie/time

Rate = 225/45

Rate = 5 cal/min

Therefore, Raquel burns Calories at a rate of 5 cal/min.

Now, we shall determine the calories burned by Raquel in 1 minutes. This is illustrated below:

Rate = 5 cal/min

Time= 1 min

Calorie =.?

Rate = Calorie /time

5 = Calorie /1

Cross multiply

Calorie = 5 x 1

Calorie = 5

Therefore, Raquel burns 5 calories in 1 minute while hiking.

Answer:

y = x₂ - 1.5 × x₁.

Step-by-step explanation:

Regression model is a technique of analysis in which a variable known as dependent variables and another variables known as the independent variables are analyzed to determine their relationship.

So, from the question given above we have that; "Suppose that participants who adhere to a particular weight loss program lose an average of 1.5 lbs per week".

Also, we are given that time = x1 (in weeks) and weight = x2 (in pounds). Therefore the regression equation is given as below;

y = x₂ - 1.5 × x₁.

Answer:

8i+8j

Step-by-step explanation:

3i+4j+5i+4j

i(3+5) + j(4+4)

Therefore 8i +8j

HAPPY TO HELP YOU

Answer:

Step-by-step explanation:

we have :

a=3i+4j

b=5i+4i

so that : a+b=3i+4j+5i+4j

=(3i+5i)+(4j+4j)

so    a+b=8i+8j=8(i+j)

Answer:

C. [tex] \sqrt {149} [/tex]

Step-by-step explanation:

Coordinates of the endpoints of the segment are (4, 4) & (-6, - 3)

By distance formula

Length of segment

[tex] = \sqrt {(4+3)^2 +(4+6)^2} [/tex]

[tex] = \sqrt {(7)^2 +(10)^2} [/tex]

[tex] = \sqrt {49 +100} [/tex]

[tex] = \sqrt {149} [/tex]

Answer: t = 4.87s

Step-by-step explanation: The vertical position y is given by

[tex]y = -16t^{2}+380[/tex]

If y at the base of the cliff equals 0, then equation is

[tex]-16t^{2}+380=0[/tex]

[tex]-16t^{2}=-380[/tex]

[tex]t^{2}=\frac{-380}{-16}[/tex]

[tex]t=\sqrt{\frac{380}{16}}[/tex]

[tex]t=\sqrt{23.75}[/tex]

t = 4.87

Since it is time we want, the negative value of the square root can be ignored. So, at the base of the cliff, the rock will hit the ground after 4.87 seconds.

Answer:

64000

Step-by-step explanation:

Answer:

64000

Step-by-step explanation:

Answer:

2x3/2-5/2

=6/-3/2

=-1

6 divide by 2 is +3 and +3 divide by - 3 equals - 1

Answer: a = [tex]\frac{u+2}{2}[/tex]

We want to isolate a. Add both sides by 2. Then we get u + 2 = 2a. To get just a, we can divide by 2 to get (u+2)/2.

Hope that helped,

-sirswagger21

Hey there! I'm happy to help!

We want to get a on one side of the equation all on its own.

Let's flip the equation around so a ends up on the left. Usually variables are supposed to be on the left.

2a-2=u

We add 2 to both sides.

2a=u+2

We divide both sides by 2.

a=(u+2)/2

We divide both u and 2 by 2 so our answer is completely simplified.

a=1/2u+1.

I hope that this helps! Have a wonderful day! :D

Answer:

10.9361

Step-by-step explanation:

The lower control limit for xbar chart is

xdoublebar-A2(Rbar)

We are given that A2=0.308.

xdoublebar=sumxbar/k

Rbar=sumR/k

xbar      R

5.8        0.42

6.1         0.38

16.02    0.08

15.95    0.15

16.12     0.42

6.18      0.23

5.87     0.36

16.2      0.4

Xdoublebar=(5.8+6.1+16.02+15.95+16.12+6.18+5.87+16.2)/8

Xdoublebar=88.24/8

Xdoublebar=11.03

Rbar=(0.42+0.38+0.08+0.15+0.42+0.23+0.36+0.4)/8

Rbar=2.44/8

Rbar=0.305

The lower control limit for the x-bar chart is

LCL=xdoublebar-A2(Rbar)

LCL=11.03-0.308*0.305

LCL=11.03-0.0939

LCL=10.9361

Answer:

The algebraic equation describing the above

X+y= x-30

Step-by-step explanation:

The initial temperature of the environment= x degrees

Temperature of the front= y degrees

the environment dropped 30 degrees, means loosed 30 degrees.

The final temperature f the environment= x-30

The algebraic equation describing the above

X+y= x-30

Answer:

3 / 13

Step-by-step explanation:

Hello!

There are 52 cards in a deck with half being red and half being black. The question ask for when a black card is drawn so we divide the total by 2

52/ 2 = 26

There are 6 black face cards in a deck so to get the probability one will be drawn we put how many there are over the total amount

6/26 we can simplify this

3 / 13

The answer is 3 / 13

Hope this helps!

Answer:

3/13

Step-by-step explanation:

In a standard 52-card deck, there are 26 black cards and 26 red cards. Of the 26 black cards, 13 are spades and 13 are clubs. Each suit has 3 face cards, Jack, Queen, and King. Therefore, there are 6 black face cards out of a total of 26 black cards.

p(face given black) = 6/26 = 3/13

Answer:

To score good marks because 1 marks can give us good life in future

Answer:

11.68ft or 11.68 feet

Step-by-step explanation:

From the above question, we are told that:

Area of the square and the Area semicircle is to be 190 ft squared.

We are also told in the question that:

The window has the shape of a square with a semicircle mounted on it.

Hence, the Diameter of the semicircle = Width of the Square

Let the Width of the square = x

Area of a square = Width²

= x²

Let the Diameter of the semi circle = x

Radius of the semi circle = Diameter of the semi circle/2 = x/2

Area of a semicircle = πr²/2

Area of a the semi Circle = π ×(x/2)² /2

= (πx²/4)/2

= πx²/8

Therefore,

Area of a square + Area of a semicircle = 190ft²

= x² + πx²/8 = 190

Cross Multiply

x² + πx² = 190

= x² ( 1 + π/8) = 190

x² = (190)/(1 + π/8)

x² = 136.42573798

x = √136.42573798

x = 11.680142892ft

Approximately x ≈ 11.68ft

Therefore, the width of the window = 11.68ft

Answer:

2/11 or approx. 18%

Step-by-step explanation:

There are 2 blue marbles out of 11 total marbles, so the probability will be 2/11.

2/11 = 0.18, or 18%

So, the odds are 2/11 or approx. 18%

Answer:

9:2

Step-by-step explanation:

9 red  and  2 blue

ways that an outcome cannot occur : how many ways it can occur

9 : 2  are the odds against a blue marble

Answer:

$1500

6 hours

Step-by-step explanation:

There is no one off fee, therefore we got (0,0) a starting point.

(1,125) is representing the first hour of rent, so 1 hour rent costs $125.

There is a direct relationship between the time and rental fee.

As a function is will be:

For x= 12, we get:

So, if f(x) = 750, then:

That means our price markup is $67.00-$50.00=$17.00

The markup price  is 34%.

It is given that cost price of the products is $ 50 and selling price of the product is  $ 67.

To find the markup price.

The profit and loss statement is a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period.

Thus, the markup in the price = [tex]\frac{S.P-C.P}{C.P} *100[/tex]

=[tex]\frac{67-50}{50} *100[/tex]

= 34[tex]%[/tex]%

So, the markup price  is 34%.

Learn more about Profit and loss here:

https://brainly.com/question/17252870

#SPJ5

Answer:

Regular Polygons

Sides - Name - Interior Angles

13 - Triskaidecagon - 152.31°

14 - Tetrakaidecagon. - 154.29°

15 - Pendedecagon. - 156.00°

16 - Hexdecagon - 157.50°

I added some more incase u need it....

Hope it helped u if yes mark me BRAINLIEST I!

Tysm!

:)

The value of a in the function's equation is 3

A function is an equation that has only one answer for y for every x. A function assigns exactly one output to each input of a specified type

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions,

equation of  parabola is :

[tex]y= a (x-h)^{2} + k[/tex]

where ,

h= horizontal coordinate of graph

k = vertical coordinate of graph

a =  the value of the coefficient

According to the question

horizontal coordinate of graph  = -2

vertical coordinate of graph = 2

[tex]y= a (x-h)^{2} + k[/tex]

[tex]y= a (x+2)^{2} + 2[/tex]

now we will take one point from  x and y value from the graph  to take out value of  coefficient a  

from graph (x,y) = (-1,5)

[tex]5= a (-1+2)^{2} + 2[/tex]

[tex]\\3= a (-1+2)^{2}[/tex]

[tex]\\3= a (1)^{2}[/tex]

[tex]a = 3[/tex]

Hence, the value of a in the function's equation is 3

To know more about equation function and parabola here :

https://brainly.com/question/26227783

# SPJ2

Answer:

24

Step-by-step explanation:

There are two triangles PQR, each with area base*half heigth = 6*2 = 12, and two times 12 is 24.

Answer:

12 cm ^2 of a single triangle

Step-by-step explanation:

area of triangle= 1/2 (l×b)

= 1/2 (4cm × 6cm)

= 1/2 (24cm^2)

= 24/2 cm^2

= 12 cm^2

and the area of both these triangle will be 24cm^2

Answer:

56 degrees

Step-by-step explanation:

They are supplementary, so they add to 180. 180 - 124 = 56.

Answer:

56 degrees

Step-by-step explanation:

They are supplementary, so they add to 180. 180 - 124 = 56.

Answer:

Step-by-step explanation:

Given a triangle has points:

(-5,1),(2,1), (2,-1)

Let us label the points:

A(2,1),

B(-5,1) and  

C(2,-1)

To find:

Distance between (−5, 1) and (2, −1) i.e. BC.

Horizontal leg AB and

Vertical leg, AC.

Solution:

Please refer to the attached diagram for the labeling of the points on xy coordinate plane.

We can simply use Distance formula here, to find the distance between two coordinates.

Distance formula :

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For BC:

[tex]x_2 = 2\\x_1 = -5\\y_2 = -1\\y_1 = 1[/tex]

[tex]BC = \sqrt{(2--5)^2+(-1-1)^2} = \sqrt{63}[/tex]

Horizontal leg, AC:

[tex]x_2 = -5\\x_1 = 2\\y_2 = 1\\y_1 = 1[/tex]

[tex]AC = \sqrt{(2-(-5))^2+(1-1)^2} = 7[/tex]

Vertical Leg,  AB:

[tex]x_2 = 2\\x_1 = 2\\y_2 = -1\\y_1 = 1[/tex]

[tex]AB = \sqrt{(2-2)^2+(-1-1)^2} = 2[/tex]

Answer:

The answer are 7, 2 and 53

Step-by-step explanation:

Answer:

$1518.31

Step-by-step explanation:

Books sold = 1307

Earning from 1307 copies = $1408.4

Earning from one copy:

Earning from 1409 copies expected:

Answer:

0

Step-by-step explanation:

To find the slope of two points, here is the formula (y2-y1)/(x2-x1)

So we have (1,2) and (4,2),

We let y2 = 2 and y1 = 2 and we let x2 = 4 and x1 = 1

So, (2-2)/(4-1) = 0/3

Our slope is 0.

-12 is the answer

Step-by-step explanation:

[tex] \frac{3x}{4} = - 9[/tex]

Firstly we have to take 4 to the R.H.S and multiply -9 with 4

[tex]3x = - 9 \times 4 [/tex]

[tex]3x = - 36[/tex]

Now, take 3 to R.H.S and divide 3 by -36

[tex]x = \frac{ - 36}{ \: \: 3} [/tex]

so after solving this we get our answer,

[tex]x = - 12[/tex]

Hope it helps u

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

Work Shown:

LCM = least common denominator

List out the prime factorization of each denominator

So we have the list of primes 2,3, and 11 that help form the denominators when we multiply some of them together.

The prime 2 shows up at most twice, so 2*2 = 4 is a factor of the LCM

The prime 3 shows up at most one time, meaning 3 is also a factor

The prime 11 shows up at most one time, so 11 is another factor

Multiply these factors to get 4*3*11 = 12*11 = 132

The LCM is 132

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

Another Approach:

Focus on 1/6 and 10/11 for now. The LCM is 66 because 6*11 = 66. We simply multiply the denominators together. Then we divide over the GCF 1 to get 66/1 = 66.

The LCM of 1/6 and 10/11 is 66

The fractions 1/6 and 10/11 are equivalent to 11/66 and 60/66 respectively

The original list of fractions updates to 11/66, 60/66, 5/12

We've gone from 3 different denominators to now 2 different denominators.

Repeat the steps of multiplying the denominators and dividing by the GCF

66*12 = 792

792/(gcf of 66 and 12) = 792/6 = 132

So the LCM of all the fractions is 132.

Answer:

First digit is 8, second digit is 4, and third digit is 2.

Step-by-step explanation:

The two number with the largest product would be the two numbers closest together.

Divide 23 in half:

23/2 = 11.5

Use the whole numbers on each side of 11.5, so you have 11 + 12 = 23

Multiply: 11x 12 = 132

Answer:

(a) The cumulative frequency curve for the data is attached below.

(b) (i) The inter-quartile range is 10.08.

(b) (ii) The 70th percentile class scores is 0.

(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.

Step-by-step explanation:

(a)

To make a cumulative frequency curve for the data first convert the class interval into continuous.

The cumulative frequencies are computed by summing the previous frequencies.

The cumulative frequency curve for the data is attached below.

(b)

(i)

The inter-quartile range is the difference between the third and the first quartile.

Compute the values of Q₁ and Q₃ as follows:

Q₁ is at the position:

[tex]\frac{\sum f}{4}=\frac{100}{4}=25[/tex]

The class interval is: 34.5 - 39.5.

The formula of first quartile is:

[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

Here,

l = lower limit of the class consisting value 25 = 34.5

(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 24

f = frequency of the class interval = 20

h = width = 39.5 - 34.5 = 5

Then the value of first quartile is:

[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

     [tex]=34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75[/tex]

The value of first quartile is 34.75.

Q₃ is at the position:

[tex]\frac{3\sum f}{4}=\frac{3\times100}{4}=75[/tex]

The class interval is: 44.5 - 49.5.

The formula of third quartile is:

[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

Here,

l = lower limit of the class consisting value 75 = 44.5

(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 74

f = frequency of the class interval = 15

h = width = 49.5 - 44.5 = 5

Then the value of third quartile is:

[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

     [tex]=44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83[/tex]

The value of third quartile is 44.83.

Then the inter-quartile range is:

[tex]IQR = Q_{3}-Q_{1}[/tex]

        [tex]=44.83-34.75\\=10.08[/tex]

Thus, the inter-quartile range is 10.08.

(ii)

The maximum upper limit of the class intervals is 69.5.

That is the maximum percentile class score is 69.5th percentile.

So, the 70th percentile class scores is 0.

(iii)

Compute the probability that a student scored at most 50 on the examination as follows:

[tex]P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}[/tex]

                                 [tex]=\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89[/tex]

Thus, the probability that a student scored at most 50 on the examination is 0.89.

Answer:DC=7

Step-by-step explanation:

As it is written △ABC = △DBC.   So the corresonding legs (the legs which are equal ) are as follows:

AC=DC       AB=DB      BC= BC

So DC=7  the same like AC