A classroom ceiling measures 6.8m by 4.7m. It is covered by boards measuring 1m by 1m
a) how many boards are needed altogether
b) How many of them will be cut
c)find the total cost of each board costs #700
​

Answer: B

Step-by-step explanation: I believe this is correct. The arrows on both run all trough the x-axis, so it would be negative infinity to positive infinity. Then, you go from open circle ( ( ) -3 to closed circle ( } ) 4.

Answer:

(3x^2 y)^4

first apply the index power to all the numbers.

3^4= 81

then you multiply the two indices.

x^2 x 4= x^8

y^4

the answer is:

81 x^8 y^4

Using the properties of half-life we calculate that approximately 22.33 grams of radium will be present after 720 years.

The half-life of radioactive element radium = 1690 years.

Time = 720 years

the formula for calculating half life is given by:

[tex]N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}[/tex]

Now we substitute the values to find the N(t) which is the amount of radium left after 720 years.

t = 720

half life = 1690

N₀ (initial mass) = 30gm

[tex]N(t)&=30\left({\frac {1}{2}}\right)^{\frac {720}{1690}[/tex]

N(t) = 22.329 gm

N(t) ≈ 22.33 gm

The half-life of a substance is the amount of time required for it to reach that point. The phrase is widely used in nuclear physics to describe how quickly unstable atoms decay radioactively or how long stable atoms remain.

Additionally, a broader definition of the term is used to characterize any exponential decay (or, very infrequently, nonexponential decay). For instance, a term used in the medical sciences is the biological half-life of drugs and other compounds in the human body.

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Answer:

12

Step-by-step explanation:

|-10+20| - |-4| + |6|

10 - 4 + 6

12

Answer: 2,666 children

Step-by-step explanation:

This player makes $3.2 M per year.  10% of his salary is $320,000

($320,000) / ($120/child) = 2,666 children

Answer:

Step-by-step explanation:

so this is a combined work problem,   both of the people are moving towards each other.  They are both doing some of the work to move towards each other.  

one is moving at 50 , the other at 60  , directly towards each other.  Now change the problem to one moving at 50+60 =110  at a destination 200 away

now you can solve this pretty easily , i'm guessing

200/110 = 1.818181

or approx.  1.82 hours

got it?

The image after the first reflection is (-x, y)

The image after the second reflection is (-x, -y)

This is equivalent to a rotation of 180°.

First, we start with a reflection across the y-axis. This type of reflection only changes the sign of the x-value of our point.

So, if we start with the point (x, y), the image after the reflection is:

(-x, y)

Now we apply a reflection across the x-axis, this one changes the sign of the y-value, then the image after the reflection is:

(-x, -y)

Notice that a change in both signs is equivalent to a 2 quadrant motion, which is equivalent to a rotation of 180°.

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The interest rate on the loan is 5.25%.

It should be noted that the formula for calculating the simple interest is given as:

Interest = (Principal × Rate × Time) / 100

In this case,

Interest = 65625

Principal = 125000

Time = 10

Interest = (Principal × Rate × Time) / 100

65625 = (125000 × R × 10)/100

Cross multiply

6562500 = 1250000R

Divide

R = 6562500 / 1250000

R = 5.25

The rate is 5.25%

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Answer: 101

Step-by-step explanation: 1+5x20 then 100+1= 101

The expression 3x+11y cannot be factorized.

What is factorization?

To factorise an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse. The same way, as the product of their factors, are the algebraic expressions written in algebra. The only difference is that in an algebraic expression, variables and integers are combined to perform mathematical operations like addition or subtraction.

Here the given expression 3x+11y didn't have any common factors.

The given expression has two variables 3x and 11y and they didn"t have any common terms.

Hence the expression 3x+11y cannot be factored.

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Given the frequency and number of possible outcomes, the number of days that must pass before it becomes probable that Janice will have had to pick up lunch at least once is 8.

Note that the probability of any of the staff at the office picking the food is 1/8.

Even if She does not pick up lunch on her first day or second, the number of days that must pass to make sure that Janice picks up lunch AT LEAST once is 1 in 8 days.

The formula to compute the probability of an event is equivalent to the ratio of favorable outputs to the total number of outputs. It is to be noted that probabilities always range between 0 and 1.

The expression is given as:

P (E) = f/O; where

P(E) is the Probability of an event E happening;

f =  The number of possible outcomes for an event (frequency)

n = Total number of outputs that are likely

Hence,

P(E) = 1/8

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The equation is 8.50x + 6y = 883.50

Number of nachos sold is 51

Number of bags of popcorn sold is 75

Given,

The cost for nachos = $8.50

The cost of a bag of popcorn = $6.00

The total amount collected = $883.50

Total number of  items sold = 126

We have to find an equation and solve to determine the number of nachos and bags of popcorn sold;

Here,

x be the number of nachos sold

y be the number of bags of popcorn sold

Then,

x + y = 126

x = 126 - y

Now,

8.50x + 6y = 883.50

Solve the equation using x as 126 -y.

That is,

8.50(126 - y) + 6y = 883.50

1071 - 8.50y + 6y = 883.50

1071 - 2.50y = 883.50

1071 - 883.50 = 2.50y

y = (1071 - 883.50) / 2.50

y = 187.50/2.50

y = 75

Now.

x = 126 - y

x = 126 - 75

x = 51.

Therefore,

The equation is 8.50x + 6y = 883.50

Number of nachos sold is 51

Number of bags of popcorn sold is 75

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The decision rule for rejecting the null hypothesis, considering the t-distribution, is of:

At the null hypothesis, it is tested if there is not enough evidence to conclude that the mean voltage for these two types of batteries is different, that is, the subtraction of the sample means is of zero, hence:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the mean voltage for these two types of batteries is different, that is, the subtraction of the sample means different of zero, hence:

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value.

Considering the significance level of 0.05, with 75 + 46 - 2 = 119 df, the critical value for the test is given as follows:

|t| = 1.9801.

Hence the decision rule is:

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Answer:

500- p=1100

400- p=800

300- p=500

200- p=200

Step-by-step explanation:

you multiply the 3 by the different numbers then subtract 400

hope it helps

Answer:

middle column P = 3(500) + -400  Last column 1100

P = 3(400) + (-400)                                                800

P = 3(300) + (-400)                                                 500

P = 3(200) + -(400)                                                200

Step-by-step explanation:

1)

1500 -400 = 100

2)

1200 - 400 = 800

3)

900 - 400 = 500

4)

600 - 400 = 200

The image of the end points X(-3 , 1) and Y(4 , -5) is

X'' = (-1 , 3) and Y'' = (5 , -4).

Given, a line segment with end points X(-3 , 1) and Y(4 , -5)

We have to find the image of the points after the given composition,

Reflection in the line y = x.

Rotation 180° about the origin.

After the reflection the image of the points X and Y be,

X' = (1 , -3) and Y' = (-5 , 4)

Now, after the rotation of the points of 180° about the origin be,

X'' = (-1 , 3) and Y'' = (5 , -4)

Hence, the image of the end points X(-3 , 1) and Y(4 , -5) is

X'' = (-1 , 3) and Y'' = (5 , -4).

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The probability of people not planning a new degree = [tex]\frac{35}{43}[/tex]  

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

And while solving these type of question we calculate the probability of a particular event.

The survey has 43 million people

Given is 8 million were planning to start a new degree program

Thus the probability of people planning a new degree program = 8 million divided by 43 million

Thus the probability of people not planning a new degree = 1 - [tex]\frac{8 million}{43 million}[/tex]

which is equal to [tex]\frac{35,000,000}{43,000,000}[/tex]

which on solving further will give us:

P ( people not planning a new degree ) = [tex]\frac{35}{43}[/tex]

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The height of the embankment is 8.19 meters

Information from the question

the length of the track is 51.1 meters

the angle of inclination is ​ 35 degrees

The height of the embankment is worked using SOH CAH TOA

The direction of movements describes a right angle triangle of

opposite = x meters

hypotenuse = 10 miles

The height is calculated using cos, CAH let the height be x

cos 35 = adjacent / hypotenuse

cos 35 = x/ 10

x = 10 * cos 35

x = 8.19 meters

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Answer:

∴ x = 70°, y = 70°, z = 40°

Step-by-step explanation:

x = 180° - 110° (adjacent angles on a straight line)

  = 70°

Since triangle PQR is an isosceles triangle,

∴ y = x = 70°

∴ z = 180° - 70° - 70° (angle sum of a triangle)

     = 40°

The expected value of the given discrete distribution is presented as follows:

E(X) = -4.7.

The expected value of a discrete distribution is obtained with the sum of each outcome multiplied by it's respective probability.

The distribution in this problem, which contains the outcomes and their probabilities, is presented as follows:

Hence the expected value of the distribution is calculated as follows:

E(X) = -7 x 0.2 - 6 x 0.1 - 5 x 0.2 - 4 x 0.2 - 3 x 0.3 = -4.7.

(each value from the distribution above, that is, -7, -6, -5, -4 and -3 was multiplied by it's respective probability and then these values were added).

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The change in the volume of water after 1 minute is 1 5/32 gallons.

Given that the volume of water in the rain barrel decreased by 4 5/8 gallons in 4 minutes.

The change after 1 minute will be:

= Total volume of water / Number of minutes

= 4 5/8 ÷ 4

= 37/8 ÷ 4

= 37/8 × 1/4

= 37 / 32

= 1 5/32

The change is 1 5/32 gallons.

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63%

First, we have to take 20.00 - 7.40 which gets us 12.60.

Then, we use the formula where we put the 12.60 on top of a fraction bar, and the 20.00 on bottom.

We do 12.60 x 100 which makes 1260.

Lastly, we divide that by the 20.00 which gets us 63.

So, Julie has 63% of her money left.

I hope this helped!!!

equation if he started his day on Wednesday with 75 end he ended with 74.32 he lost -0.68 of his share hope this helped there a lot of extra information in the question

An equation is written as  expressions, connected by an equals signal ("=").[2] The expressions on the two facets of the equals signal are referred to as the "left-hand side" and "right-hand side" of the equation. Very regularly the right-hand side of an equation is assumed to be zero. Assuming this doesn't lessen the generality, as this can be realized through subtracting the right-hand side from each facets.

The most common sort of equation is a polynomial equation (commonly known as also an algebraic equation) wherein the 2 facets are polynomials. the edges of a polynomial equation incorporate one or greater terms

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32 is the next term in the arithmetic sequence of 24,16,8,0,...

To find out what is the next term of the arithmetic sequence

24, 16, 8, 0, ...

To show the explicit equation:

We have an arithmetic sequence because the difference between the terms is constant:

0 → 8: Δ → 8

8 → 16: Δ → 8

16 → 24: Δ → 8

From this the next term is simply:

24 + 8 = 32

And this sequence can be explicitly written as:

[tex]a_{n} = a_{1}(n-1)d[/tex]

Where:

[tex]a_{n}[/tex] = nth term

[tex]a_{1}[/tex] = first term

d = distance between the terms

n = any index number

Therefore we have:

[tex]a_{n} = 1.(n-1)8 = 8.(n-1)\\\\a_{n} = 8. (n-1)[/tex]

Hence the answer is 32 is the next term in the arithmetic sequence of 24,16,8,0,...

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The two way table to display the relative frequency by row is:

            Lasagna orders

                           veggie        meat         total      

Tomato sauce     44.871%     55.128%   100%

cream sauce        76.67%       23.33%    100%

Given:

Tomato sauce = 35 veggie + 43 meat

= 78

cream sauce = 46 veggie + 14 meat

= 60

veggie % in tomato sauce = 35 * 100/78 = 3500/75 = 44.871%

meat % in tomato sauce = 43 * 100 / 78 = 4300/78 = 55.128%

veggie % in cream sauce = 46 * 100 / 60 = 4600/60 = 76.67%

meat % in cream sauce = 14 * 100 / 60 = 1400/60 = 23.33%

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Answer:

-5

Step-by-step explanation:

The number of values of x to be excluded is 2.

To find out the values of x that must be excluded in the expression

(x+9)(x-5) as follows:

The value of x is 2.

We are given to find the number of value of x that must be excluded in the expression  below:

E = (x+9)(x-5)

We have to exclude those values of x for which the expression E becomes undefined.

Since E is a rational expression, so the becomes undefined only when the denominator becomes 0.

That is,

(x+9)(x-5) = 0

= x+9 = 0         x-5 = 0

= x = -9            x = 5

Therefore, we need to exclude the values x = -9  and  x =5.

So, there are two values of x to be excluded from the given expression.

Hence the answer, the number of values of x to be excluded is 2.

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The slope of the line in the image is a zero slope.

The slope of a line can be defined as the ratio of a line's vertical change to the line's horizontal change, which is rise/run or change in y / change in x.

An horizontal line has horizontal change but no vertical change. Therefore, no matter the horizontal change of the line, the slope of a horizontal line would always be zero. Therefore, horizontal lines have zero slope.

The line in the image is a horizontal line, therefore, the slope is neither positive nor negative, but a zero slope.

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Answer:

  ∠2 = ∠4 = ∠6 = ∠8 = 114°

  ∠1 = ∠3 = ∠5 = ∠7 = 66°

Step-by-step explanation:

You want to know the measures of all of the angles where transversal t crosses parallel lines m and n. ∠4 is given as 114°.

Where a transversal crosses parallel lines, all of the acute angles are congruent, and all of the obtuse angles are congruent. The obtuse and acute angles form linear pairs, so are supplementary.

In the given figure, the acute angles are numbered using odd numbers, and the obtuse angles are numbered using even numbers.

∠2 = ∠4 = ∠6 = ∠8 = 114°

∠1 = ∠3 = ∠5 = ∠7 = 180° -114° = 66°

If two cubes have sides of length 5 cm and 6cm. The ratio of their respective surface​ areas is 36 : 25.

Using this formula to find the ratio

Ratio of their surface area  = a /a'

Where:

a = 6

a' =5

Let plug in the formula

Ratio of their surface area  = 6a² /6a'²

Ratio of their surface area  = 6(6)² / 6(5)²

Ratio of their surface area  = 36 / 25

Ratio of their surface area  = 36 : 25

Therefore the ratio is 36 : 25.

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Answer:

Factored form is the form of the equation.