What is the solution to the following equation? (4 points)

2(3x − 7) + 18 = 22

a
1

b
3

c
5

d
6

Using proportions, it is found that the better deal, on a per ounce basis, is given by:

For each option, the costs per ounce are given by:

\(C_a = \frac{4.2}{30} = 0.14\)

\(C_b = \frac{3.6}{24} = 0.15\)

\(C_c = \frac{6.3}{42} = 0.15\)

\(C_d = \frac{6.3}{42} = 0.15\)

Due to the smaller cost, option A is the better deal.

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Answer:

196

Step-by-step explanation:

70% multiply by 4/5(80%) which is 56%

56% times 350

none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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Answer: k=8

Step-by-step explanation: im pretty sure i dont remember

Answer:

1330.4 cm³

Step-by-step explanation:

radius = 11/2 = 5.5 cm

height = 14 cm

volume = area × height

Answer:

\(x = \sqrt{3 \frac{ - 1}{3} } \)

The denominator of the formula for the variance of a sample is given as follows:

N - 1.

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

The terms are named as follows:

The formula for the variance of a sample is given as follows:

\(s^2 = \frac{sum (X - \overbar{X})^2}{N - 1}\)

Hence the denominator is the bottom term, which is of N - 1.

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The area in units of square meter is 2,090,318.4 sq cm,  under the given condition that  a house has a floor area of 2,250 square feet. So , the correct option from the following is  Option B.

To convert 2,250 square feet to square centimeters, we can use the conversion factor of 1 square foot = 929.0304 square centimeters⁵. Therefore,

2,250 sq ft = 2,250 x 929.0304 sq cm/ sq ft = 2,090,318.4 sq cm.

The area in units of square meter is 2,090,318.4 sq cm,  under the given condition that  a house has a floor area of 2,250 square feet. So , the correct option from the following is  Option B.

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Answer:

12a3 + 2a2 + 23a + 18

Step-by-step explanation:

Vertical multiplication works well when you have a binomial times a trinomial.

Multiply 2 times the trinomial and get 8a2 - 4a + 18 then multiply 3a times the trinomial to get 12a3. -6a2 + 27a

Then combine like terms.

The product of the givens expressions is 12a³ + 2a² + 23a + 18.

The product of the givens expressions is obtained by multiplying all the variables in the bracket as shown below.

(3a + 2)(4a² – 2a + 9) = 3a(4a² – 2a + 9) + 2(4a² – 2a + 9)

= 12a³ - 6a² + 27a + 8a² - 4a + 18

simplify by collecting similar terms together

= 12a³ + 2a² + 23a + 18

Thus, the product of the givens expressions is 12a³ + 2a² + 23a + 18.

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Answer:

mostly to measure interest rates

Answer:

slope = 9 y-intercept = -5/2

Step-by-step explanation:

since slope form is y=mx+b we know that m= slope and b=y-intercept. since 9 is in place of the m that shows that 9 is the slope. since 5/2 is in the b place you would think the y-intercept would be 5/2 but since the equation is - 5/2 instead of + 5/2 it would be + (-5/2) making the y-intercept negative. hope this helped. :)

The frequency of the allele for non-tasting PTC in the population is 0.09 or 9%.

To determine the frequency of the allele for non-tasting PTC in a population where the frequency of PTC tasters is 91%, we can use the Hardy-Weinberg equation. The Hardy-Weinberg principle describes the relationship between allele frequencies and genotype frequencies in a population under certain assumptions.

Let's denote the frequency of the allele for taster individuals as p and the frequency of the allele for non-taster individuals as q. According to the principle, the sum of the frequencies of these two alleles must equal 1, so p + q = 1.

Given that the frequency of PTC tasters (p) is 91% or 0.91, we can substitute this value into the equation:

0.91 + q = 1

Solving for q, we find:

q = 1 - 0.91 = 0.09

Therefore, the frequency of the allele for non-tasting PTC in the population is 0.09 or 9%.

It's important to note that this calculation assumes the population is in Hardy-Weinberg equilibrium, meaning that the assumptions of random mating, no mutation, no migration, no natural selection, and a large population size are met. In reality, populations may deviate from these assumptions, which can affect allele frequencies. Additionally, this calculation provides an estimate based on the given information, but actual allele frequencies may vary in different populations or geographic regions.

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Answer:

∠A + ∠B= 180°

98°+∠B = 180

∠B= 82°

Step-by-step explanation:

well, let's move like the crab, backwards, let's start with b), then we'll do a)

b)

\({\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=75 \end{cases}\implies 75=ab^2 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=5\\ y=9375 \end{cases}\implies 9375=ab^5\implies 9375=ab^{2+3}\implies 9375=ab^2 b^3\)

\(\stackrel{\textit{substituting from the 1st equation}}{9375=\underset{ab^2}{(75)} b^3}\implies \cfrac{9375}{75}=b^3\implies 125=b^3 \\\\\\ \sqrt[3]{125}=b\implies \boxed{5=b}\hspace{5em}\stackrel{\textit{we know that}}{75=ab^2}\implies 75=a5^2\implies 75=25a \\\\\\ \cfrac{75}{25}=a\implies \boxed{3=a}\hspace{5em} {\Large \begin{array}{llll} y = 3(5^x) \end{array}}\)

a)

\(\begin{cases} x=0\\ y=j \end{cases}\implies j=3(5^0)\implies j=3(1)\implies j=3 \\\\\\ \begin{cases} x=4\\ y=k \end{cases}\implies k=3(5^4)\implies k=3(625)\implies k=1875\)

Answer:

16 + 64 + 64 are the 3 sides.

Step-by-step explanation:

There are two sides that are 4 times the third side.

Let the 3rd side = x

4x + 4x + x = 144 inchines

9x = 144 inches

x = 144/9

x = 16 inches.

So the base (which is the smallest side) = 16 inches.

One of the two sides remaining is 4x = 4*16 = 64

The other side = 64

Check

64 + 64 + 16 = 144 as it should.

Answer:

Step-by-step explanation:e

The stratified random sampling is a method of various strata are selected from the sample. So, the right choice for answer is option(c).

The four probability sampling methods mainly applied in research methods include simple random sampling, cluster sampling, stratified sampling, and systematic sampling. In certain situations, we need to remove the sampling bias, and for that, we opt for stratified random sampling. Here we talking about stratified random sampling. A method of probability sampling (where all members of the population have an equal chance of being included) Population is divided into 'strata' (sub populations) and random samples are drawn from each. Therefore, the required choice is option (c), that is various strata are selected from the sample.

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Step-by-step explanation:

you are really struggling with such simple things ? you only need to type it into your calculator, and you have your answer in 2 seconds.

instead you are posting the question here, then you wait, if there is an answer, then you copy the answer back to your work ...

so, please tell me, what is your real problem with these questions ?

there are 52 weeks in a year.

instead of 2 bottles of $15 each she now only buys 1 bottle of $15 per week.

she saves $15 per week (one bottle instead of 2).

so, in a year she saves

15×52 = $780

Hello!

The answer is 28.8, When finding the Volume of a shape, you multiply all numbers.

Answer:

picture #1 - 50.27 square units

picture #2 - 113.10 square units

picture #3 - 380.13 square units

Step-by-step explanation:

picture #1 - area = πr^2 -> π*4^2 = 50.27 square units

picture #2 - area = πr^2 -> π*6^2 = 113.10

picture #3 - area = πr^2 -> π*11^2 = 380.13

Answer:

The answer is A

Step-by-step explanation:

This figure is a cylinder and the surface area formula of a cylinder is 2 pi rh + 2pi r^2

The argument is valid using the indirect or short method of proof because the conclusion follows logically from the premises.

The argument is valid. The Indirect Method for proving a syllogism is a technique that looks at whether the syllogism's conclusion is false and whether this leads to a false premise.

If a false conclusion leads to a false premise, the syllogism is sound and valid.

When considering the validity of the argument, there are two main techniques: direct and indirect.

Direct method: The direct method is used to validate the argument by evaluating it in terms of its logical truth.

The premises' validity is used to assess the soundness of the conclusion.

Indirect method: The indirect method is used to invalidate the argument by evaluating it in terms of its logical falsehood.

The conclusion's invalidity is used to assess the unsoundness of the premises.

The argument is valid using the indirect or short method of proof because the conclusion follows logically from the premises.

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Answer:

-23 divided by -7

Step-by-step explanation:

Answer:

-7 - x < -2/3

Step-by-step explanation:

The difference between −7 and a number x

-7 - x

is no more than −2/3.

-7 - x < -2/3

We have proved the given argument using the method of Conditional Proof (CP) as part of the whole process.

In the given proof, we have to show that ~P -> ~R is true. We can prove it by using the method of Conditional Proof (CP) as a part of the whole process. Let us begin with the first proof.
Do the 1st proof by using CP with ~P as AP
Assumption: ~P
C: ~R
1: R -> (L & S)        Given
2: (L V M) -> P        Given
3: ~P                  Assumption
4: ~(L V M)            From 3 and 2 by Modus Tollens
5: ~L & ~M             From 4 by De Morgan's Law
6: ~L                  From 5 by Simplification
7: ~S                  From 1 and 6 by Modus Ponens
8: ~(L & S)            From 6 and 7 by Conjunction
9: ~R                  From 1 and 7 by Modus Ponens
10: ~P -> ~R           From 3 to 9 by CP
[44-2.2] Do the 2nd proof by using CP with R as AP
Assumption: R
C: ~P -> ~R
1: R -> (L & S)        Given
2: (L V M) -> P        Given
3: ~P                  To be proved
4: L V M               To be proved
5: L                   Assumption
6: L V M               From 5 by Addition
7: P                   From 6 and 2 by Modus Ponens
8: ~S                  From 1 and 5 by Modus Ponens
9: ~(L & S)            From 8 by De Morgan's Law
10: ~L V ~S            From 9 by De Morgan's Law
11: ~L                 Assumption
12: ~(L & S)           From 11 and 8 by Conjunction
13: ~L V ~S            From 12 by De Morgan's Law
14: ~S                 From 10 and 13 by Disjunctive Syllogism
15: (L & S) & P        From 7 and 5 by Conjunction
16: (L & S)            From 15 by Simplification
17: Contradiction      From 16 and 9
18: ~R                  From 17 by Negation Introduction
19: ~P -> ~R           From 3 to 18 by CP

The given argument needs to be proved using CP, where we have to show that ~P -> ~R is true. The first proof is done with ~P as an assumption, while the second proof is done with R as an assumption. The method of Conditional Proof is a method of proving a statement where we assume the negation of the consequent. The negation of the consequent is added as an assumption, and the premises are used to derive the negation of the antecedent. Once the negation of the antecedent is derived, we can discharge the assumption of the negation of the consequent, thereby proving the statement. In the given argument, we have used the method of CP to prove that ~P -> ~R. In both the proofs, we have used the premises and the assumptions to derive the conclusion. In the first proof, we assumed ~P and used the premises to derive ~R. In the second proof, we assumed R and used the premises to derive ~P -> ~R. Hence, we have proved the given argument using the method of CP.

Therefore, we have proved the given argument using the method of Conditional Proof (CP) as part of the whole process. We used two proofs in the argument, one with ~P as an assumption and the other with R as an assumption. We have shown that ~P -> ~R is true using the given premises and the method of CP.

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Answer:

Yes

Step-by-step explanation:

From the origin means from the centre or middle but about a vertex is from a named point.

Answer:22.1%

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

By substituting 1 into the equation for x, both sides will equal 8.

Answer:

add 9 to both sides

Step-by-step explanation:

because half of 6 is 3 and its square is 9

Answer:

48/52

Step-by-step explanation:

The probability of picking up an ace in a 52 deck of cards is 4/52 since there are 4 aces in the deck. The odds of picking up any other card is therefore \(52/52 - 4/52 = 48/52.\)

I hope this helps and have a great day!

1.  The simultaneous solution of the given equations is X=12/5 and Y=4/5

2.1)The combination of X and Y that will yield the optimum for this problem is X=0 and Y=3.3.

2)The combination of X and Y that will provide a minimum for this problem is X=3 and Y=0.

To find the simultaneous solution of the given equations 4X+3Y=12 and 2X+4Y=8, we can use the method of elimination, also known as the addition method. Multiplying the second equation by 2, we get 4X+8Y=16.

Now, we can subtract the first equation from the second equation: 4X+8Y - (4X+3Y) = 8Y - 3Y = 5Y and 16 - 12 = 4. Thus, 5Y=4 or Y = 4/5.

Substituting this value of Y in any of the two equations, we can find the value of X. Let's substitute this value of Y in the first equation: 4X+3(4/5)=12 or 4X

= 12 - (12/5)

= (60-12)/5

= 48/5.

Thus, X = 12/5. Hence, the simultaneous solution of the given equations is X=12/5 and Y=4/5.2. To find the optimal values of X and Y that will maximize the objective function Z=$10X+$50Y, we need to use the method of linear programming.

First, let's plot the feasible region defined by the given constraints:We can see that the feasible region is bounded by the lines 3X+4Y=12, 2X+5Y=10, X=0, and Y=0.

To find the optimal solution, we need to evaluate the objective function at each of the corner points of the feasible region, and choose the one that gives the maximum value.

Let's denote the corner points as A, B, C, and D, as shown above. The coordinates of these points are: A=(0,3), B=(2,1), C=(5/2,0), and D=(0,0). Now, let's evaluate the objective function Z=$10X+$50Y at each of these points:

Z(A)=$10(0)+$50(3)

=$150, Z(B)

=$10(2)+$50(1)

=$70, Z(C)

=$10(5/2)+$50(0)

=$25, Z(D)

=$10(0)+$50(0)=0.

Thus, we can see that the maximum value of Z is obtained at point A, where X=0 and Y=3. Therefore, the combination of X and Y that will yield the optimum for this problem is X=0 and Y=3.3.

To find the combination of X and Y that will provide a minimum for the problem Minimize Z=X+5Y subject to: 4X+3Y≥12 and 2X+5Y≥10, we need to use the same method of linear programming as above.

First, let's plot the feasible region defined by the given constraints:We can see that the feasible region is bounded by the lines 4X+3Y=12, 2X+5Y=10, X=0, and Y=0.

To find the optimal solution, we need to evaluate the objective function Z=X+5Y at each of the corner points of the feasible region, and choose the one that gives the minimum value.

Let's denote the corner points as A, B, C, and D, as shown above.

The coordinates of these points are: A=(3,0), B=(5,1), C=(0,4), and D=(0,0).

Now, let's evaluate the objective function Z=X+5Y at each of these points:

Z(A)=3+5(0)=3,

Z(B)=5+5(1)=10,

Z(C)=0+5(4)=20,

Z(D)=0+5(0)=0.

Thus, we can see that the minimum value of Z is obtained at point A, where X=3 and Y=0. Therefore, the combination of X and Y that will provide a minimum for this problem is X=3 and Y=0.

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The y-intercept of a function happens when the function "cuts" the y-axis.

This can be calculated as the value of the function f(x) when x=0.

Then, if we replace x by 0, we get the y-intercept:

The y-intercept for this function is f(0)=18.