whats 1 and 3/4 times 4 and 1/6?

Answer:

Step-by-step explanation:

Let R = Richard, T = Teo.

Richard and Teo have a combined age of 41. This means that if you add their ages together you get 41:

R + T = 41

We are also told Richard is 5 years older than twice Teo's age:

R = 2T + 5

You can substitute " R " into R + T = 41

R + T = 41

2T + 5 + T = 41

3T + 5 = 41

Subtract 5 from both sides

3T = 41 - 5

3T = 36

Divide both sides by 3 to find T.

T = 36/3 = 12

We know that R + T = 41, so

R = 41 - T

R = 41 - 12

R = 29

Answer:

Richard is 29 and Teo is 12

Step-by-step explanation:

let Teo's age be n then Richard is 2n + 5 ( 5 more than twice Teo's age )

Thus their combined ages are

n + 2n + 5 = 41 , that is

3n + 5 = 41 ( subtract 5 from both sides )

3n = 36 ( divide both sides by 3 )

n = 12

Then

Teo is 12 years old and Richard is 2(12) + 5 = 24 + 5 = 29 years old

The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

Find out more information about difference quotient here:

https://brainly.com/question/18270597

#SPJ4

Scenario 1: At least one ball is red.

In this scenario, we have four possible outcomes: RR (both red), RB (one red and one blue), BR (one red and one blue), and BB (both blue). Since we know that at least one ball is red, the outcome BB is not possible. Therefore, we only need to consider the outcomes RR, RB, and BR.

Out of the three possible outcomes, only one outcome is favorable (RR), where both balls are red. Hence, the probability that both balls are red, given that at least one is red, is 1/3.

Scenario 2: A ball is picked at random and it is painted red.

In this scenario, we assume that one ball has been randomly chosen and it is painted red. Now, we need to consider the two possible outcomes: RR (both red) and RB (one red and one blue).

Out of the two possible outcomes, one outcome is favorable (RR), where both balls are red. Hence, the probability that both balls are red, given that a ball is randomly picked and painted red, is 1/2.

To summarize:

The probability that both balls are red, given that at least one is red, is 1/3.

The probability that both balls are red, given that a ball is picked at random and it is painted red, is 1/2.

learn more about possible outcomes here

https://brainly.com/question/29181724

#SPJ11

Answer:

49 dogs

Step-by-step explanation:

the 4 part of the ratio relates to 28 cats , then

28 ÷ 4 = 7 ← value of 1 part of the ratio , then

7 parts = 7 × 7 = 49 ← number of dogs at the shelter

Answer:

49 dogs

Step-by-step explanation:

given that the ratio of cats : dogs is 4 : 7

which means that :

for every 4 cats, there are 7 dogs

if we express this as a unit rate, this also means that :

for every 1 cat, there are 7/4 dogs.

given that there are 28 cats, therefor the number of dogs

= number of cats x unit rate

= 28 x (7/4)

= 49 dogs

The base angle for the isosceles triangle is 53°.

Any triangle with two sides that have the same length is said to be an isosceles triangle. If the two sides of a triangle are congruent, then the angle across from them must likewise be, according to the theorem that explains the isosceles triangle. As a result, the two angles of an isosceles triangle that are on opposite sides with equal numbers are equal in size.

Given base length = 6 and leg length = 5

draw a perpendicular to the base that divides the base into equal parts,

as shown in the image attached

let the base angle be Ф,

and using a cosine formula for the base angle

cosФ = base/hypotenuse

from construction  base = 3 and hypotenuse = 5

cosФ = 3/5

Ф = cos⁻¹(3/5)

Ф = 53.13°

Ф = 53° (approx)

Hence the base angle is 53°

Learn more about the isosceles triangle;

https://brainly.com/question/2456591

#SPJ1

Answer:

4 hours

Step-by-step explanation:

y = total cost

x = per hour

Equation:

y = 200.97 + 30.39x

322.53 = 200.97 + 30.39x

322.53 - 200.97 = 30.39x

121.56 = 30.39x

x = 4

We will use a correction factor of 0.5. Then:

P(X<=25.5)

The normal distribution mean:

The normal distribution standard:

Then:

From the normal distribution table, the probability is 0.239

The correlation analysis indicates a moderate positive relationship between Column X and Column Y.

To perform correlation analysis, we can use the Pearson correlation coefficient (r) to measure the linear relationship between two variables, in this case, Column X and Column Y. The value of r ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

Here are the steps to calculate the correlation coefficient:

Calculate the mean (average) of Column X and Column Y.

Mean(X) = (10+6+39+24+35+12+33+32+23+10+16+16+35+28+5+22+12+44+15+40+46+35+28+9+9+8+35+15+34+16+19+17+21) / 32 = 24.4375

Mean(Y) = (37+10+18+12+11+34+26+9+42+24+40+1+39+24+42+7+17+17+27+47+35+14+38+18+17+22+12+30+18+43+24+45+24) / 32 = 24.8125

Calculate the deviation of each value from the mean for both Column X and Column Y.

Deviation(X) = (10-24.4375, 6-24.4375, 39-24.4375, 24-24.4375, ...)

Deviation(Y) = (37-24.8125, 10-24.8125, 18-24.8125, 12-24.8125, ...)

Calculate the product of the deviations for each pair of values.

Product(X, Y) = (Deviation(X1) * Deviation(Y1), Deviation(X2) * Deviation(Y2), ...)

Calculate the sum of the product of deviations.

Sum(Product(X, Y)) = (Product(X1, Y1) + Product(X2, Y2) + ...)

Calculate the standard deviation of Column X and Column Y.

StandardDeviation(X) = √[(Σ(Deviation(X))^2) / (n-1)]

StandardDeviation(Y) = √[(Σ(Deviation(Y))^2) / (n-1)]

Calculate the correlation coefficient (r).

r = (Sum(Product(X, Y))) / [(StandardDeviation(X) * StandardDeviation(Y))]

By performing these calculations, we find that the correlation coefficient (r) is approximately 0.413. Since the value is positive and between 0 and 1, we can conclude that there is a moderate positive relationship between Column X and Column Y.

For more questions like Correlation click the link below:

https://brainly.com/question/30116167

#SPJ11

Answer:

\(Density = 1.1546\ kg/pint\)

Step-by-step explanation:

Given

\(Mass = 7\ lb\)

\(Cups = 5.5\)

Required

Determine the density in Kg/Pint

Density is calculated as thus:

\(Density = \frac{Mass}{Volume}\)

\(Density = \frac{7\ lb}{5.5\ cups}\)

Convert pound to kg

\(Density = \frac{7/ 2.205\ kg}{5.5\ cups}\)

\(Density = \frac{3.17515\ kg}{5.5\ cups}\)

Convert cups to pint

\(Density = \frac{3.17515\ kg}{5.5/2\ pint}\)

\(Density = \frac{3.17515\ kg}{2.75\ pint}\)

\(Density = 1.1546\ kg/pint\)

Any value or values for a variable or variables that make an equation or inequality true is called a solution

In this question, we have been given a statement 'Any value or values for a variable or variables that make an equation or inequality true is called a ________'

We need to complete the given statement.

We know that an equation is a statement which has equal symbol between two mathematical expressions.

And the inequality is nothing but the relationship between two algebraic expressions that are not equal.

A value of the variable which satisfy the equation ( or inequality)  or make the equation true  is called root or solution of the equation  ( or inequality).

Therefore, the complete statement is, 'Any value or values for a variable or variables that make an equation or inequality true is called a solution.'

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ4

The output of the statement "cout << "x+y=" << x+y << endl;" would be "x+y=7". The output of the statement "cout << "z/x=" << z/x << z/x << endl;" would be "z/x=33"

The given int variables x = 2, y = 5 and z = 6. In this question, we are asked to find the output of each of the following statements.b. `cout ≪"x+y="≪x+y≪ endl`

When we add two integers 2 and 5 then the sum is 7.

Therefore, the output is given as `x+y=7`.c. `cout ≪< n z/x= n ≪z/x≪≪ endl`When we divide 6 by 2 then we get 3. Therefore, the output is given as `z/x=3`.d. `cout ≪ "2 times " ≪x≪≪ " =" ≪2 ∗ x≪ endl`

When we multiply 2 with 2 then the product is 4.

Therefore, the output is given as `2 times 2 = 4`.

Therefore, the outputs of the given statements are as follows:b. `x+y=7`c. `z/x=3`d. `2 times 2 = 4`.

Hence, option b is correct.

To learn more about “variable” refer to the https://brainly.com/question/28248724

#SPJ11

The law that deals with the truth value of propositions p and q is the Law of Syllogism, which allows us to draw conclusions based on two conditional statements.

The law that deals with the truth value of propositions p and q is called the Law of Syllogism. The Law of Syllogism allows us to draw conclusions from two conditional statements by combining them into a single statement. It is also known as the transitive property of implication.

The Law of Syllogism states that if we have two conditional statements in the form "If p, then q" and "If q, then r," we can conclude a third conditional statement "If p, then r." In other words, if the antecedent (p) of the first statement implies the consequent (q), and the antecedent (q) of the second statement implies the consequent (r), then the antecedent (p) of the first statement implies the consequent (r).

This law is an important tool in deductive reasoning and logical arguments. It allows us to make logical inferences and draw conclusions based on the relationships between different propositions. By applying the Law of Syllogism, we can expand our understanding of logical relationships and make deductions that follow from given premises.

It is worth noting that the terms "law of detachment" and "law of deduction" are sometimes used interchangeably with the Law of Syllogism. However, the Law of Syllogism specifically refers to the transitive property of implication, whereas the terms "detachment" and "deduction" can have broader meanings in the context of logic and reasoning.

for such more question on propositions

https://brainly.com/question/870035

#SPJ8

Answer:

9 hours

Step-by-step explanation:

You have to add both hours to get the total amount. So 3+6=9

Answer:

9 hours

Step-by-step explanation:

Stacy worked on the house 9 hours because she worked 3 hours before lunch and 6 hours after lunch. 6+3=9

Answer:

true

Step-by-step explanation:

The function y = e³r is a solution to the differential equation y" + 2y' - 15y = 0. The function y = c₁e^x + c₂xe is a solution to the differential equation y" - 2y + y = 0.

(a) To prove that y = e³r is a solution to y" + 2y' - 15y = 0, we need to substitute y and its derivatives into the differential equation and verify if the equation holds true. Let's calculate the first and second derivatives of y = e³r:

y' = 3e³r  (by the chain rule)

y" = 9e³r (by differentiating y' with respect to r)

Now, substitute y, y', and y" into the differential equation:

9e³r + 2(3e³r) - 15(e³r) = 9e³r + 6e³r - 15e³r = 0

Hence, the function y = e³r satisfies the given differential equation.

(b) For the differential equation y" - 2y + y = 0, let's substitute y = c₁e^x + c₂xe and its derivatives into the equation:

y' = c₁e^x + c₂e^x + c₂xe^x (using the product rule)

y" = c₁e^x + c₂e^x + c₂xe^x + c₂e^x + c₂xe^x (differentiating y' with respect to x)

Simplifying the equation:

(c₁e^x + c₂e^x + c₂xe^x + c₂e^x + c₂xe^x) - 2(c₁e^x + c₂xe^x) + (c₁e^x + c₂xe^x) = 0

By combining like terms, we get:

(c₁ + 2c₂)e^x + (4c₂)e^x = 0

Since the equation holds true for any values of c₁ and c₂, the function y = c₁e^x + c₂xe is a solution to the given differential equation.

Learn more about differential equation here:

https://brainly.com/question/32524608

#SPJ11

The evidence from the text that supports the conclusion that Brutus and Cassius are in conflict are:

“Brutus, bay not me. / I’ll not endure it.”

“Away, slight man!”

We have,

“Brutus, bay not me. / I’ll not endure it.”

“Away, slight man!”

Both these lines show that Brutus and Cassius are having a heated argument and are in conflict.

The first line is Cassius telling Brutus not to attack him, and the second line is Cassius insulting Brutus by calling him a "slight man".

Thus,

The evidence from the text that supports the conclusion that Brutus and Cassius are in conflict are:

“Brutus, bay not me. / I’ll not endure it.”

“Away, slight man!”

Learn more about  Brutus and Cassius here:

https://brainly.com/question/11196132

#SPJ1

Answer:

a. (x² + y²)² = (x² - y²)² + (2xy)²

b. The conjecture works in all cases.

c. Sides of 119, 120, and 169

Step-by-step explanation:

a. Equation that models this conjecture

x² + y² = sum of squares

x² - y² = difference of square

  2xy = twice the product of the integers

If these are the sides of a right triangle then

(x² + y²)² = (x² - y²)² + (2xy)²

b. Test the conjecture

(i) Try x = 2, y = 1

(2² + 1²)² = (2² - 1²)² + (2×2×1)²

       5² = 3² + 4²

      25 = 9 + 16

(ii) Try x = 3, y = 1

(3² + 1²)² = (3² - 1²)² + (2×3×1)²

      10² = 8² + 6²

    100 = 64 + 36

(iii) Try x = 3, y = 2

(3² + 2²)² = (3² - 2²)² + (2×3×2)²

       13² = 5² + 12²

     169 = 25 + 144

The conjecture appears to work in all cases.

c. A possible triangle

We must have one side greater than 100. That means,  

x² > 100 or x >1 0.

                                      Let x = 12

                               One side = 12² + y²

                  The second side = 12² - y²

The third side must have 2xy > 100

                                        24y > 100

                                            y > 4.2

                                      Try y = 5

                              (12² + 5²)² = (12² - 5²)² + (2 × 12 × 5)²

                                       169² = 119² + 120²

So, one right triangle could have sides of 119, 120, and 169.

Furthermore, these sides have no common factors.

Check:

 169² = 119² + 120²

28561 = 14161 + 14400

28561 = 28561

Answer:

c = 60

Step-by-step explanation:

A triangle = 180 degrees

180-(15+105)=c

c=60

Answer:

negative i think :/

Step-by-step explanation:

Answer:

3 < M - N < 9

Step-by-step explanation:

First, let's write the inequalities for these two numbers.

"a number greater than -3 and less than -2"

 -3 < N < -2

"a number greater than 1 and less than 6"

1 < M < 6

We want to subtract the first one to the second one, so we want to get:

M - N

Because this is a subtraction, the lower bound of the subtraction happens when we have the minimum value of M and the maximum value of N.

Then the minimum value of M - N happens when:

M = 1

N = -2

(notice that M can't be equal to 1, and N can't be equal to -2, we just do this to find the lower bound)

Then the lower bound is:

M - N = 1 - (-2) = 3

We already got:

3 < M - N

For the upper bound, we need to find the difference between the largest value of M, and the lowest value of N

This is:

M = 6

N = -3

M - N = 6 - (-3) = 9

Then:

M - N < 9

If we take both of our results, the possible values of the subtraction are given by:

3 < M - N < 9

The result of subtracting a number greater than -3 and less than -2 from a number greater than 1 and less than 6 is mathematically given as

3 < M - N < 9

Question Parameter(s):

-3 < N < -2

1 < M < 6

therefore,

subtraction for lower bound

M - N = 1 - (-2)

M - N = 3

3 < M - N

subtraction for upper bound

M - N = 6 - (-3)

M - N = 9

M - N < 9

In conclusion,  the possible values after subtraction are

3 < M - N < 9

Read more about Inequality

https://brainly.com/question/19491153

The expression "x -16.5" is expressed as "x less 16.5". Option B shows the correct expression.

The expression is defined as a set of terms combined using the operations addition, subtraction, multiplication, or division.

The given expression is \(x - 16.5\).

The expression shows that 16.5 is subtracted from x. The resulting value is 16.5 less than x.

If the expression is expressed in words, it would be "x minus 16.5" or "x is reduced by 16.5"

Hence we can conclude that the expression "x -16.5" is expressed as "x less 16.5". Option B shows the correct expression.

To know more about the expression, follow the link given below.

brainly.com/question/13947055.

The declaration states that the value of Arc EFC = 253°.

A measure is indeed a quantitative concept used to express how large a collection is. Each unique measure represents a different method for determining how large a collection is. It would initially appear that a set's cardinality is the only logical way to determine its number.

We can tell we are working with a circular that has 360 degrees because of the connection.

We can infer that we have it if we look at that file.

Arc EFC

Arc CD

Arc DE

And everything together give us 360,

Arc EFC + Arc CD + Arc DE = 360

If we examine the figure again, we can see that the central angle of an intercepted arc is identical to the arc's measure.

Arc CD is 90 degrees since the central angle is 90 degrees given

Arc DE is 17 degrees

Arc EFC + Arc CD + Arc DE = 360

If we input all the figures

Arc EFC + 90 + 17 = 360

Arc EFC + 107 = 360

Arc EFC = 360 - 107

Arc EFC = 253

Therefore, Arc EFC = 253°

To know more about Measure visit:

https://brainly.com/question/25716982

#SPJ1

The correct questions is:

Circle O, and are diameters. Arc ED measures 17°. Circle O is shown. Line segments F C and A E are diameters. Line segments C O and B O are radii. Point B is between points A and C, and point C is between points E and C. Angle D C is a right angle. What is the measure of Arc E F C? 107° 180° 253° 270°

Answer:

3 Cups of flour

Step-by-step explanation:

1 batch of cookies = 1 cup of flour

2 batch of cookies = 2 cups of flour

3 batch of cookies = 3 cup of flour

I hope i helped you :)

Answer:

Step-by-step explanation:

4 plus 8 is 12 plus 5 is 17. then add the months 5 plus 6 is 11 plus 8 is 19, 19 is one year and 7 months so the answer is 18 years old and 7 months.

Answer: 18 years and 7 months

Step-by-step explanation:5+8+4= 17 and 8+6+5= 19

17 years and 19 months aka 18 and 7 months

(a) We can draw a sketch of the trapezoid as shown in the image attached.

(b) z = 4

(c) BC = 32 units

(a) Since ABCD is an isosceles trapezoid with legs AB and CD. And with Base BC. Thus, we can draw a sketch of the trapezoid as shown in the image attached.

(b)  Since the legs of an isosceles trapezoid are equal in measure. Thus, we can say:

AB = CD

6z - 5 = 4z + 3

6z - 4z = 3 + 5

2z = 8

z = 8/2

z = 4

(c) BC = 7z +4

Put z = 4 in BC. That is:

BC = 7z +4

BC = 7(4) +4

BC = 32 units

Learn more about trapezoid on:

https://brainly.com/question/1410008

#SPJ1

Answer: y = -4/5x + 2

Step-by-step explanation:

Parallel is same slope diff y intercept (b)

4x + 5y = 3

-4x

/5

Minus 4x and divide by 5

y = -4/5x  + 3/5

6 = -4/5(-5) + b

solve b = 2

The major assumption in factor analysis (but not PCA) is that the observed variables are caused by a smaller number of underlying, unobserved (latent) variables, which are called factors.

Factor analysis and principal component analysis (PCA) are both techniques used for data reduction and dimensionality reduction. However, they differ in their assumptions and goals.

In factor analysis, the focus is on identifying the underlying latent variables (called factors) that explain the observed correlations among a set of variables. The major assumption in factor analysis is that the observed variables are caused by a smaller number of underlying factors. These factors cannot be directly measured, but are inferred from patterns of correlations among the observed variables. The goal of factor analysis is to extract these factors and to estimate how much each factor contributes to each observed variable.

In contrast, PCA is a technique that focuses on finding a linear combination of the original variables that explain the maximum amount of variance in the data. The major assumption in PCA is that the observed variables are not caused by any underlying factors, but are simply linearly related to each other. The goal of PCA is to find a set of orthogonal (uncorrelated) principal components that capture the maximum amount of variance in the data.

Therefore, the major assumption in factor analysis (but not PCA) is that there are underlying latent variables (factors) that cause the observed correlations among the variables.

Visit to know more about Factor analysis:-

brainly.com/question/12495119

#SPJ11

Answer: C Polly bought a cracker for $4 and then bought a parrot for $2

-$6

Step-by-step explanation:

Word problem which can be modeled by the addition of two negative numbers :

Option A:

Selling or making a sales will yield a positive value

OptionB:

Purchasing is negative, however, reselling is positive

OptionC:

Purchasing a cracker (c) for $4 = - 4

Purchasing a parrot (p) for $2 = - 2

Hence, both are negative

c + p

-4 + (-2)

= - $6

Option D:

Selling is positive ; purchasing is negative