12 less than a number is equal to the product of 7 and that number. Convert into an
equation and find the number?
Please explain it step by step

Answer:

12

Step-by-step explanation:

The square root of 144 is defined as the only positive real number such that, multiplied by itself, it is equal to 144.

The square root of 144 can be written as (144)1/2. Like this

(144) 1/2 = (12 × 12)1/2

(144) 1/2 = [(12)2]1/2

(144) 1/2 = (12)2/2

(144) 1/2 = (12)1

Later

√144 = 12

Hey there!

√144

≈ √12^2

≈ √12 * 12

≈ √144 = 12

Therefore, your answer is: 12

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

To find the number of days it will take for Juliana's investment to grow, we can use the formula for simple interest

I = P * r * t.

I = interest earned
P = principal amount (initial investment)
r = interest rate per year (in decimal form)
t = time in years In this case,

Juliana's principal amount (P) is $3,300, the interest rate (r) is 6.25% or 0.0625, and she wants to reach $3,450. We need to solve for t. $3,450 = $3,300 * 0.0625 * t Divide both sides of the equation by ($3,300 * 0.0625) to isolate t:
t = $3,450 / ($3,300 * 0.0625)
t = 17 So it will take Juliana approximately 17 days for her investment to grow to $3,450.

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Answer:

triangle 4

Step-by-step explanation:

Translation is moving a shape without rotating or resizing. So in this case it'll be 4.

Answer:

x = 41

And, the  number of CDs in Walter's collection is 41

Step-by-step explanation:

The computation is shown below;

Given that

The number of CDs in Jimmy collection = x

The number of CDs in Alex's collection = 4x

And, The total number of CDs in both collections is 205

So, the equation is

x + 4x = 205

5x = 205

x = 41

The alex collection is

= 4 × 41

= 164

So, the walter collection is

= 164 ÷ 4

= 41

Tomatoes are typically lighter than cucumbers since the mean weight for tomatoes is less than the mean weight for cucumbers.

Answer:

Lighter, less

Step-by-step explanation:

The mean is also known as the average. This means that it is the sum of all values divided by the total number. Therefore it is said that on average, tomatoes weigh less than cucumbers.

The function 1/\(r^2\) can be expressed in terms of the spherical Bessel functions of the first kind, which are a family of solutions to the spherical Bessel differential equation.

The expansion involves a combination of the delta function and the first two spherical Bessel functions, j_0(r) and j_1(r). Specifically, the expansion can be written as (1/2)*[pi * delta(r) + (1/r)*d/d(r)(r * j_0(r)) + (1/\(r^2\))*d/d(r)[\(r^2\) * j_1(r)]]. This expansion is valid for all values of r except for r=0, where the first term dominates. The spherical Bessel functions are commonly used in physics, particularly in the context of scattering problems and wave propagation.

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Answer:

341 players

Step-by-step explanation:

31 x 11

= 341 players

Answer:

54 marbles

Step-by-step explanation:

The question is a word problem leading to a simultaneous equation

Let 'x' represent the initial number of marbles with Sam, and let 'y' represent the initial number of marbles with Mary,

If Mary gives Sam 5 marbles, we have;

x + 5 = 2 × (y - 5)...(1)

If Sam gives Mary 4 marbles, we get;

x - 4 = y + 4...(2)

From equation (1), we get;

x + 5 = 2 × (y - 5) = 2·y - 10

x = 2·y - 10 - 5 = 2·y - 15

x = 2·y - 15...(3)

From equation (2), we have;

x - 4 = y + 4

∴ x = y + 4 + 4 = y + 8

x = y + 8...(4)

Equating the two values of 'x' in equation (3), and equation (4), we get;

2·y - 15 = y + 8

2·y - y = 8 + 15 = 23

∴ y = 23

From equation (4), we get;

x = y + 8 = 23 + 8 = 31

x = 31

The total number of marbles they have altogether = x + y

However, x + y = 23 + 31 = 54

Therefore;

The total number of marbles they have altogether = 54 marbles.

Answer:

Option B is correct

Step-by-step explanation:

Both the exponential functions f(x) = e(x - 4) and g(x) = (1/2)e(x - 4) have e(x - 4) as their base function. This base function shows a horizontal shift for both functions of 4 units to the right.

We can see that g(x) is produced by multiplying the base function by 1/2 in order to compare the two functions. The graph is vertically compressed as a result of this multiplication, but the horizontal shift is unaffected.

Since the horizontal shift is unchanged, the only difference between the two functions is the vertical compression factor.

Answer:

79.8

Step-by-step explanation:

The volume of the solid generated by revolving the region about the given line. the region in the first quadrant bounded above by the line y=2 square root 3 is \(16\pi /3 (\sqrt[]{3} - 1).\)

To find the volume of the solid generated by revolving the region in the first quadrant bounded above by the line y=2 square root 3, we need to know the axis of rotation. Assuming the axis of rotation is the x-axis, we can use the method of cylindrical shells.

The region bounded above by the line y=2 square root 3 and the x-axis is a triangle with base length 2(2/√3) and height 2√3. Thus, the area of the region is A = (1/2)(2(2/√3))(2√3) = 4.

To generate the solid, we revolve the region about the x-axis. Consider a horizontal strip of thickness dx at a distance x from the y-axis. The radius of the cylindrical shell generated by this strip is r = 2√3 - x, and the height of the shell is the same as the height of the region, h = 2√3.

The volume of the shell is given by V = 2πrhdx = 4π(2√3 - x)dx.

Integrating from x = 0 to x = 2√3, we have:

\(V = \int\limits{ { 0^(^2^\sqrt[]{3} )} 4\pi (2\sqrt[]{3} - x)}dx\)
 = \(4\pi (2\sqrt{3x} - x^2/2)|0^(^2^\sqrt{3} )\)
 = 16π/3 (√3 - 1)

Therefore, the volume of the solid generated by revolving the region about the x-axis is 16π/3 (√3 - 1).

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Using the exponential regression feature of the calculator to find the equation of the regression line, we get that \($$y = 0.8996 e^{1.3759x}.$$\)

Given data, $$\begin{array}{|c|c|} \hline x & y\\ \hline 1 & 2.20\\ 2 & 3.60\\ 3 & 5.90\\ 4 & 9.70\\ 5 & 15.90\\ 6 & 26.00\\ \hline \end{array}.$$

The equation of the form is y = 1 + aebx;

Thus, the required equation is \($$y = 1 + 0.8996 e^{1.3759x}.$$\)

Finally, putting x = 7, we get

\($$y = 1 + 0.8996 e^{1.3759(7)} \approx 156.76.$$\)

Thus, the required equation is\($$y = 1 + 0.8996 e^{1.3759x}.$$\)Finally, putting x = 7, we get

\($$y = 1 + 0.8996 e^{1.3759(7)} \approx 156.76.$$\)

So, the value of y at x = 7 is approximately 156.76.

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Answer:its a lot of money

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

2((-1)(3)-7) = x

-1•3 first, then subtract that by 7 = -10

then multiply by 2 = -20

Using strong induction, we can prove that the square root of -2 is irrational by showing that it cannot be expressed as a fraction of coprime odd integers.

To prove that √-2 is irrational using strong induction, we need to show that for any natural number n, if the square root of -2 can be expressed as a fraction a/b, where a and b are coprime integers, then a and b must be odd.

We can start by using the base case, n = 1. Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers.

Now, let's assume that for all n ≤ k, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. We want to prove that this also holds for n = k+1.

Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers with a and b odd. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd.

By strong induction, we have proven that for any natural number n, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Therefore, √-2 is irrational.

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The item which is closest in size to one mole of gas at STP is C) A microwave

A mole is the quantity of matter contained in a body.

We know that at STP the volume of gas occupied by one mole of a gas at STP is 22.4 dm³.

Now, we have 4 items.

Let us assume that each item is a cube. Also, since 22.4 dm³ is the volume of the cube, its length is

L = ∛22.4 dm³

=  ∛(22.4 × 10³) cm³

= 28.2 cm

So, ithe item that is comparable to this length is the microwave.

So, the item is C. A microwave

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Answer:

\( \huge \boxed{ \red{ \boxed{\begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} }}}\)

Step-by-step explanation:

distribute tan(θ):

=>tan²(θ)-(tan(θ)+√3tan(θ))+√3=0

remove parentheses:

=>tan²(θ)-tan(θ)-√3tan(θ)+√3=0

so this equation is now in standard form i.e ax²+bx+c=0

we can solve by factoring as we solve quadratic equation

factor out tanθ:

=>tan(θ)(tan(θ)-1)-√3tan(θ)+√3=0

factor out -√3:

=>tan(θ)(tan(θ)-1)-√3(tan(θ)-1)=0

group:

=>(tan(θ)-√3)(tan(θ)-1)=0

separate it as two different equation:

\( \implies \begin{cases} \tan( \theta) - 1 = 0 \\ \tan( \theta) - \sqrt{3} = 0 \end{cases}\)

add 1 and √3 to both sides to first and second equation respectively:

\( \implies \begin{cases} \tan( \theta) - 1 + 1 = 0 + 1 \\ \tan( \theta) - \sqrt{3} + \sqrt{3} = 0 + \sqrt{3} \end{cases} \)

\( \implies \begin{cases} \tan( \theta) = 1 \\ \tan( \theta) = \sqrt{3} \end{cases} \)

\( \therefore \begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} \)

The given expression is

We will multiply at first -5 by 3

Then we will multiply x^2 by x^4 by adding their powers

And multiply y by 1 as there is no y in the second bracket, then

The answer is C

You can get the answer by reciprocating the multiplying factor of 10%

88*10/11

= 80 kg

Therefore, Hamid's original weight was 80 kgs

Answer:

x=-8

Step-by-step explanation:

4(1/2x+7)=12

Divide each side by 4

4/4(1/2x+7)=12/4

(1/2x+7)=3

Subtract 7 from each side

1/2x+7-7=3-7

1/2x = -4

Multiply each side by 2

1/2x*2 = -4*2

x = -8

Answer:

-8

Step-by-step explanation:

Divide both sides by 4 which will give you 1/2x+7=3

Then multipy both sides by 2 which will then give you x+14=16

Then move the constant = x=6-14

6-14 is -8 which will give you x=-8

Answer:

X³ – 3x² – 9x – 5

= x³ + x² – 4x² – 4x – 5x – 5

= x²( x + 1) – 4x ( x + 1) – 5(x + 1)

= (x + 1)(x² – 4x – 5)

= (x + 1)(x² -5x + x – 5)

= (x + 1)(x – 5) (x + 1)

hence, (x +1), (x -5) and (x +1) are the factors of given polynomial .

Was this answer helpful?

Answer:

5x + 4

Step-by-step explanation:

1/2 (10z + 8)

= 1/2 x 10z + 1/2 x 8

= 5z + 4

Hope this helps!!

There are 662 union members working for the company.

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

Let's use "x" to represent the ratio multiplier, which will allow us to find the actual number of union and nonunion members.

According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that for every 4 union members, there are 5 nonunion members.

We can set up a proportion to find the value of x:

4/5 = x/207

To solve for x, we can cross-multiply:

4 × 207 = 5 * x

828 = 5x

x = 828/5

x = 165.6

Since we cannot have a fraction of a person, we must round this value to the nearest whole number.

Now we can use x to find the actual number of union members:

Number of union members = 4x

Number of union members = 4 × 165.6

Number of union members = 662.4

hence, Rounding this value to the nearest whole number, we can say that there are 662 union members working for the company.

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For the following scenario where a researcher wanted to test the ratings of three different brands of paper towels with 7 reviewers each, you would utilize Friedman's rank test.

For the given scenario, the appropriate test to use would be the Friedman's rank test. This is because we have three different brands of paper towels, and each brand is rated by 7 reviewers.

The Friedman's test is used to determine if there are significant differences among the groups in a repeated measures design, where the same individuals are rated on multiple occasions. Therefore, it is the appropriate test for this scenario where the ratings are collected from multiple reviewers for each brand.

This test is also appropriate because there are more than two related groups being compared (three brands of paper towels), and the data is likely ordinal (ratings). The Wilcoxon sign rank test is typically used when comparing only two related groups.

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Answer:

x=9

Step-by-step explanation:

Let total bundle=x

Morning edition of the daily sun=1/3x

=x/3

Afternoon edition of the daily sun=2

That leaves 2x/3 - 2, of which

x/3 - 1 are regional

1 is local

1 from another state

Sum everything

x = x/3 + 2 + x/3 - 1 + 1 + 1

x=2x/3 +3

x-2x/3=3

3x-2x/3=3

x/3=3

Cross product

x=3×3

x = 9

The test statistic is at α = 0.10 we have sufficient evidence that means weight is given by μ = 132 lb.

What is p-value?

The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, presuming that the null hypothesis is true.

As given,

State the hypothesis,

Ha: μ = 132

Ha: μ ≠ 132 (two failed test)

Test satisfies:

As σ is unknown we will use t-test satisfies

t = (x - μ)/(s/√n)

Substitute values,

t = (137 - 132)/(14.2/√20)

t = 1.57

t satisfies is 1.57.

Critical values,

P(t < tc) = P(t < tc) = 0.05

using t table at df = 19

tc = ±1.729

So value is tc = (-1.729, 1.729)

P-value:

P(t > ItstatI) = p-value

P(t > I1.57I) = p-value

Using t-table

p-value = 0.1329

given

α = 0.10

So, p-value < α

Do not reject Null hypothesis.

Conclusion:

At α = 0.10 we have sufficient evidence that means weight is given by μ = 132 lb.

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The doctor computed test statistic to test his claim that the average body temperature is less than 98.6 degrees Fahrenheit.

Test statistic is a statistic which is derived from the sample to test whether to accept the null hypothesis or to accept the null hypothesis.

A sample is data which is a subset of population. That is, it is the smaller, version of a large group.

As we have been given in the question the doctor wanted to test his claim, so he did a hypothesis test. And for the hypothesis test he calculated a random data from the sample that was collected from the population data which is known as the test statistic.

Hence doctor computed the test statistic to test his claim.

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The Original price of the item  was $400.

Percentage can be defined as a number that denotes hundredth part of any quantity.

For Example , 50%of 30 =\(\frac{50}{100} *30=\frac{1500}{100} =15\).

In the given question

Amount paid by Joyce = $120

Let the original price =x

Percent of original price = 30%

According to the given Question

30% of x =120

\(\frac{30}{100} *x=120\\ \\ x=\frac{120*100}{30}\\ \\ \\ x=400\)

Therefore , the Original price of the item  was $400.

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