In one month, Sally worked 6 more hours than Harold. Harold worked 2 times as many hours as Nora. Together they worked 81 hours. How many hours did each person work?

Answer:

7.9

Step-by-step explanation:

this would just be sqrt (8^2 - 1^2) or sqrt 63 or about 7.9

The ladder reaches 7.9 meters when the bottom of the ladder is x = 1m from the building.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

It is given that:

A ladder 8 m long is leaning against a building.

From the data given, a right angle triangle is formed:

Applying the Pythagoras theorem:

Building high² = 8² - 1²

Building high² = 63

Building high = 7.9 meters

Thus, the ladder reaches 7.9 meters when the bottom of the ladder is x = 1m from the building.

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The maximum value of the objective function is 26 and the minimum is -10

The objective function is given as:

z=−3x+5y

The constraints are

x+y≥−2

3x−y≤2

x−y≥−4

Start by plotting the constraints on a graph (see attachment)

From the attached graph, the vertices of the feasible region are

(3, 7), (0, -2), (-3, 1)

Substitute these values in the objective function

So, we have

z= −3 * 3 + 5 * 7 = 26

z= −3 * 0 + 5 * -2 = -10

z= −3 * -3 + 5 * 1 =14

Using the above values, we have:

The maximum value of the objective function is 26 and the minimum is -10

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Answer:

(C U B )=(q,x,y)

(C U B )n A=q

Answer: THE ANSWER IS A) $860

Step-by-step explanation: I GOT A 100 ON THE TEST

Answer:

refer to the attachment

samples confidence intervals needed is Option C 136.

According to the Empirical rule, if data exists normally distributed then about 68% of the population lies within one standard deviation from the mean.

We assume that the mean of a normally distributed population exists at 300, and 200 simple random samples exist drawn from the population.

Number of simple random samples, n= 200

By Empirical rule, approximately 68% of 200 samples’ confidence intervals we would expect to have the population mean.

Required number of samples = 68% of 200

= 0.68 x 200 = 136

The required number of samples = 136

Therefore, the correct answer is option C) 136.

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Answer:

x = 117

Step-by-step explanation:

Foremost, we know that the three angles of the triangle always add up to 180 degrees.

So, there are two sides which are 27 degrees and 36 degrees, we need to find the third one's degree.

Add 27 and 36 (27 + 36 = 63)

Two sides equal 63.

Then, subtract 180 - 63 = 117

So the third angle's measurement is 117 degrees. The answer is 117.

To check, add 117 + 27 + 36 = 180

Hope it helps.

See below for the algebraic expressions of the scenarios.

The given parameters are:

Scenario 1

Represent the speed with x.

So, we have:

Speed = Distance/Time

The time is given as:

Time = 10 minutes

Since he did not stop at all;

The speed is

x = 2400/10

Multiply both sides by 10

10x = 2400

The above expression represents the scenario 1.

Scenario 2

Represent the speed with x, and time with t

So, we have:

Speed = Distance/Time

The time to reach halfway is given as:

Time = 6 minutes

He stopped for 1 minute, before continuing at the same initial speed

So, the total time it 13 minutes

The speed is represented as:

x = 2400/13

Multiply both sides by 13

13x = 2400

The above expression represents the scenario 2.

Scenario 3

Represent the speed with x, and time with t

So, we have:

Speed = Distance/Time

The time to reach halfway is given as:

Time = 6 minutes

He stopped for 1 minute, before continuing at twice the initial speed

So, the total time is

t = 6 + 1 + 1/2 * 6 minutes

t = 10 minutes

The speed is represented as:

x = 2400/10

Multiply both sides by 10

10x = 2400

The above expression represents the scenario 3.

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The solution of the given expression is 9*[tex]x^{4}[/tex]/100.

GIven an expression equal to 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].

We have to simplify the expression in which variable comes only once.

Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.

The given fraction is 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].

When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.

=27[tex]x^{4}[/tex]/300

Now divide numerator an denominator by 3.

=9[tex]x^{4}[/tex]/300

Hence the expression 27[tex]x^{12} /300x^{8}[/tex] will look like [tex]9x^{4} /100[/tex] after simplifying.

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Answer:

[tex]Simplify:\sqrt\frac{27x^{12} }{300x^{8} }[/tex]

[tex]O \frac{9}{100}x^{4}[/tex]

✔ [tex]\frac{3}{10} x^{2}[/tex]

[tex]O \frac{27}{300} x^{4}[/tex]

[tex]O\frac{9}{10} x^{2}[/tex]

Answer:

x = 7.43

Step-by-step explanation:

X - 2.13 = 5.3

add -2.13 to both sides

x -2.13+2.13 = 5.3 + 2.13

-2.13 + 2.13 cancel out and 5.3 +2.13 equals 7.43

therefore x =7.43

check your work by substituting 7.43 for x

7.43 - 2.13 = 5.3

Due to length restrictions, we kindly invite to read the explanation of this question for further details about the table and graph of the function.

In this problem we must plot the graph of a function on a Cartesian plane. The procedure is summarized below:

After following the procedure, we have the following result:

Input, x             x + 4                Output, y             (x, y)

   - 2               - 2 + 4                     2                    (- 2, 2)

     0                 0 + 4                     4                     (0, 4)

     2                 2 + 4                     6                     (2, 6)

     4                 4 + 4                     8                      (4, 8)

     6                 6 + 4                    10                      (6, 10)

     8                 8 + 4                    12                      (8, 12)

Lastly, we plot the graph of the linear function.

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Answer:

no

Step-by-step explanation:

Answer:

Step-by-step explanation:

6(3x-5)≤2(9x+7)+10

divide by 2

3(3x-5)≤9x+7+5

3(3x-5)≤9x+12

divide by 3

3x-5≤3x+4

-5≤4

which is true.

Answer:

[tex] \pink{\maltese{ \text{BODMAS \:Full \: Form \: }}}[/tex]

The expression (48-24)÷3×4 as per BODMAS rule.

(48-24)÷3×4

=24÷3×4

=8×4

=32

Now,

The given question is,

Simplify:

[tex] \displaystyle{ \frac{7}{8} \div 5 \frac{1}{3} \times \frac{24}{7} }[/tex]

[tex] \displaystyle{ = \frac{7}{8} \div \frac{16}{3} \times \frac{24}{7} }[/tex]

[tex] \displaystyle{ = \frac{ \cancel{7} \times 3 \times \cancel{24} \: {}^{3} }{ \cancel{8 } \times 16 \times \cancel{7}} }[/tex]

[tex] \displaystyle{ = \frac{3 \times 3}{16} }[/tex]

[tex] \displaystyle{} = \frac{9}{16} [/tex]

Thus,the final answer is 9/16.

Solution -:

[tex] \frac{7}{8} \div 5 \frac{1}{3} \times \frac{24}{7} [/tex]

Let's begin-

solve,,,

Now,,According to BODMAS rule fist we divide ,

[tex] \frac{7}{8} \times \frac{3}{16} \times \frac{24}{7} \\[/tex]

Now , we multiple

[tex] \frac{3 \times 3}{16} \\ \\ = \frac{9}{16} [/tex]

and this is our final answers

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

Division → Multiplication → Addition → Subtraction

Using the binomial distribution, the probabilities are given as follows:

a) 0.37 = 37%.

b) 0.5065 = 50.65%.

c) 0.3260 = 32.60%.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the fixed parameter is:

p = 0.37.

Item a:

The probability is P(X = 1) when n = 1, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{1,1}.(0.37)^{1}.(0.63)^{0} = 0.37[/tex]

Item b:

The probability is P(X = 3) when n = 3, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.37)^{3}.(0.63)^{0} = 0.5065[/tex]

Item c:

The probability is P(X = 2) when n = 4, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{4,2}.(0.37)^{2}.(0.63)^{2} = 0.3260[/tex]

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Answer:

Step-by-step explanation:

hello : here is a solution

Answer:

B=37

H=66

Step-by-step explanation:

Use algebra and find the answer.

The complete factorization of the equation 81x² - 100 is; (9x - 10)(9x + 10)

We are given the quadratic equation;

81x² - 100

Now, according to quadratic identities, we know that;

(a + b) * (a - b) = a² - b²

Now, our equation can also be expressed as;

81x² - 100 = 9²x² - 10²

Thus, applying the quadratic identity gives us;

(9x + 10)(9x - 10)

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Answer:

4.13

Step-by-step explanation:

Using sine ratio where it states that sine of a measurement is equal to ratio of opposite of measurement to hypotenuse (slant side/side with slope)

From the question, our opposite is x, hypotenuse is given as 15 units and the measurement is 16°. Apply the formula:

[tex]\displaystyle{\sin 16^{\circ} = \dfrac{x}{15}}[/tex]

Move 15 to multiply sin(16°):

[tex]\displaystyle{15\sin 16^{\circ} = x}[/tex]

Go ahead and input the value in a calculator since it's not a special triangle - a measurement that can be found using hand method - after you find the value, round it to 2 decimal places:

[tex]\displaystyle{x = 4.13456033...}[/tex]

Therefore, after rounding to 2 decimal places, the answer is:

[tex]\displaystyle{x=4.13}[/tex]

Therefore, the value of x is 4.13 units.

The conditional relative frequency for female students who prefer playing sports is 34%.

The table of values is given as:

                        Sports   Dancing Row totals

Male students      18             16        34

Female students  18             35       53

Column totals       36            51         87

Mason's calculation is given as:

P = 21%

This is gotten by

18/87 = 21%

The above represents the joint relative frequency of female students who prefer playing sports.

To calculate the conditional relative frequency, he should divide 18 by the row total.

So, we have

18/53 = 34%

Hence, the conditional relative frequency for female students who prefer playing sports is 34%.

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The experiment is illustrated below.

A. The type of experimental design is a completely randomized design experiment where experimental units of 200 female subjects which are allocated randomly to say 4 treatment groups with each treatment group consist of 50 female patients.

Here the treatment used is low-intensity shock therapy which is also factor or explanatory variable. After administrating above treatment for a period of say 2-3 weeks, the response in pain reduction can be measured among all patients in 4 treatment groups by comparing their earlier pain level for reduction in pain.

If the study consist of 100 male and female patients, the experimental design can be changed into randomized block design by blocking subjects by gender.

The above design can be double blinded by not letting either the patients or lab technicians aware about which treatment groups, each of these subjects are experimented against to keep the data confidential.

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answer

symbolic materials ?

Work Shown:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.2 + 0.8 - 0.07

P(A or B) = 0.93

Answer:

(a) B' U U = { f,g,h,p,q,r}

(b) B ∩ U = {g,q,r}

Step-by-step explanation:

Greetings !

(a) B/c B'= {X: X∈U and X∉B}

thus,B'= {f,h,p}

B' U U= {f,h,p} U {f,g,h,p,q,r}

= {f,g,h,p,q,r}

(b) B ∩ U= {g,q,r}

The estimated value of 5,016 exists 1 / 264 ≈ 0.00379.

Fractions describe the regions of a complete or group of objects. A fraction contains two regions. The number on the top of the line exists named the numerator. It describes how many equivalent regions of the real or group stand accepted. The number below the line exists named the denominator. It exhibits the total number of equivalent regions the whole exists divided into or the total number of the exact objects in a group.

The value of 5,016 can be simplified by using a fraction

Consider a denominator 19, then

19 divided by 5,016, then we get

19 and 5016 have a common divisor of 19.

then, we get

19 / 5016 = 1 / 264

Now, you need to divide.

1 / 264 ≈ 0.00379

Therefore, the estimated value of 5,016 exists 1 / 264 ≈ 0.00379.

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Answer:

|NT| = 25

Step-by-step explanation:

The four sides of this square all have the same length.  Thus, 5x = 10x - 25, which, in turn, becomes 25 = 5x, giving us x = 5.  The length of NT is 5(x), or |NT| = 25.

The amount after 1 year is $7280 and the amount after two year is $8153.

Given that $6500 is placed in an account that pays 12% interest compounded each year.

Compounding is the addition of interest to the principal of a loan or deposit, or in other words, interest on principal plus interest.

Compounded interest=12%

Principal amount=$6500

Time period = 1 year

[tex]A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]

where P is Principle amount, r is annual interest, n is number of times the interest compounded monthly, t is number of years

Here P=6500, r=12%, n=1, t=1

Substitute these values in the formula, we get

A=6500(1+(0.12/1))¹⁽¹⁾

A=6500(1+0.12)¹

A=6500×1.12

A=7280

Now we have to calculate for two years.

That is if n=2 , then

A=6500(1+(0.12/1))¹⁽²⁾

A=6500(1+0.12)

A=6500×1.2544

A=8153.6

Hence, the amount for one year and two year when $6500 is placed in an account that pays 12% interest compounded is $7280 and $8153.60.

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Answer:

a) 10/21 b) 5/21 c)1/21

Step-by-step explanation:

a) your have 7 choice and 5 or them or red, 5/7.  You do not replace the red marble, so for your second draw, you now only have 6 choices and of those 6 choices only 4 of them are now red or 4/6 or 2/3.  We multiple these two numbers together:

5/7(2/3) = 10/21

b) For the first draw, you have 5 red marbles available out of a total 7 marbles or 5/7.  The second draw now only has 6 marbles and 2 of them or yellow to make 2/6 or 1/3 (simplified).  We multiply these together.

5/7(1/3) =5/21

c)  I am assuming that you are still selecting 2 marbles.  The first draw would be 2/7.  This time I am selecting yellow and there are only 2 choices for yellow.  My next draw will only have 6 marbles and only 1 of them will be yellow, so 1/6.  We multiply these together

2/7(1/6) = 2/42 or 1/21