Write an algebraic equation for the following problem and then solve it.
The population of a country in 2015 was estimated to be 321.4 million people. This was an increase of 17% from the population in 1990. What was the population of the country in 1990?
The algebraic equation is _=321.4

The sets that number 343 belongs to are:

So, 343 is:

Therefore, the sets that number 343 belongs to are:

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To prove ∠1 = ∠3.

Parallel lines are a grouping of two or more lines that all lie in the same plane but never cross. Both of them have the same slope and are equally spaced apart.

Numerous pairs of angles are created whenever any two parallel lines are intersected by a third line known as a transversal. The other angles are supplementary while some are congruent (equal). The parallel lines L1 and L2, which are divided by a transversal, can be seen in the following figure.

Given : [tex]l||k , m||n[/tex]

∠1= ∠2 {alternate interior angles}

∠2=∠3 {corresponding angles are equal because k is parallel to l }

Thus from the above two equations :

∠1 = ∠3

Hence, proved .

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The expression with rational exponent in radical form as √x⁵ Cassie's expression is correct.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have been given that four students have rewritten the expression with rational exponent in radical form as shown.

As per Sammi's expression: VE

This is an incorrect expression

As per Malik's expression: √7³

This is an incorrect expression

As per Cassie's expression: √x⁵

This is the correct expression

As per Casey's expression: √T

This is an incorrect expression

Thus, the expression with rational exponent in radical form as √x⁵ Cassie's expression is correct.

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The number of units of each type that should be purchased to maximize the number of people processed is 6 unit A and 6 unit B.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Any mathematical object has a symbol, and that symbol is called a variable. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

Given that,

The budget for new metal detectors is $75,000.

Maximum of 18 security guards available for each shift.

Unit A costs $5000, requires 1 security guard and can process 300 people per hour.

Unit B costs $7500, requires 2 security guards and can process 500 people per hour.

Let x = unit A

Let y = unit B

N = 300x + 500y

Here, 5000x + 7500y ≤ 75000

X+2y≤ 18

y≥4

x≥0

Hence,

(0, 9) = 300(0) + 500(9)

(0, 9) = 4500

(0, 4) = 300(0) + 500(4)

(0, 4) = 2000

(9, 4) = 300(9) + 500(4)

(9, 4) = 4700

since,

(6, 6) = 300(6) + 500(6)

(6, 6) = 4800

Therefore, flywithus should buy 6 unit A and 6 unit B to maximize the number of people processed.

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Answer:

7.5 or 7 1/2

Step-by-step explanation:

A recipe requires 2 1/2 of flour. How much flour is needed to triple the recipe?​

3 × 2 1/2 can be written as 3 × 2.5 = 7.5 or 7 1/2

Answer: 26 degrees

Step-by-step explanation: Count from -15 to 11 or add them up.

h divide by 4 = 9

Mathematically, this can be written as

h / 4 = 9

Introduce cross multiplication

h = 4 x 9

h = 36

The answer is 36

Based on the calculations, the value of x in this geometric sequence is equal to √2

Mathematically, the nth term of a geometric sequence is given by this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio of this geometric sequence as follows:

r = a₂/a₁ = a₃/a₁

Substituting the given parameters into the common ratio formula, we have;

1/√X + 1 = √x - 1/1

Taking the square of both sides, we have:

1/x + 1 = x - 1/1

Cross-multiplying, we have:

(x + 1)(x - 1) = 1

x² - x + x - 1 = 1

x² - 1 = 1

x² = 1 + 1

x² = 2

x = √2

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The numbers from least to greatest in ascending order is 1/5 , 0.35 , 12/25 , 0.5 , 4/5.

The organization of numbers known as ascending order places the smallest number before the greatest.

The numbers can be written in decimals as:

0.5 , 0.2 , 0.35 , 0.48 and 0.8.

The numbers written from least to greatest in ascending order is :

0.2 < 0.35 < 0.48 < 0.5 < 0.8

Hence the numbers will be:

1/5 , 0.35 , 12/25 , 0.5 , 4/5.

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By solving a system of equations, we can see that there are 17 children and 8 parents in the room.

Let's define the variables:

x = number of children.

y = number of parents.

We know that there are 9 more children than parents, then:

x = y + 9

And there is a total of 25 people, so:

x + y = 25

So we have a system of equations:

x = y + 9

x + y = 25

Replacing the first equation into the second one, we get:

(y +9) + y = 25

2y + 9 = 25

2y = 25 - 9 = 16

y = 16/2 = 8

then the value of x is:

x = y + 9 = 8 + 9 = 17

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Answer:

[tex]x = \frac{910000}{207} [/tex]

Answer:

n=3/2 and 6

Step-by-step explanation:

4n²-30n+36=0

2n²-15n+18=0

2n²-12n-3n+18=0

2n(n-6)-3(n-6)=0

(2n-3)(n-6)=0

2n-3=0 or n-6=0

n=3/2 or n= 6

factorization approach ✨

Answer:

y = -1x

gradient = -1

rise/run= +10-20/-10+20

            = -10/10

            = -1

y intercept is 0 as line is passing through 0 on y axis

For verification:

input any pair of x and y values in y = mx + b

10=-1(-10)+b

10=10+b

b= 10-10

b=0

Equation:

y = -1x

1. (-6, 8)

2. -2

3. 4

Using the definition of the Laplace transform:

[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_0^t \tau \cos(3\tau) \, d\tau\right) e^{-st} \, dt[/tex]

Reverse the order of integration. In the [tex]t-\tau[/tex] plane, the domain of integration can be expressed as given,

[tex]D = \left\{(t,\tau) ~:~ 0\le t<\infty \text{ and } 0\le \tau\le t\right\}[/tex]

or equivalently as

[tex]D' = \left\{(t,\tau) ~:~ \tau \le t < \infty \text{ and } 0 \le \tau < \infty\right\}[/tex]

Then the Laplace transform is

[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_\tau^\infty e^{-st} \, dt\right) \tau \cos(3\tau) \, d\tau \\\\ ~~~~~~~~ = \frac1s \int_0^\infty e^{-s\tau} \tau \cos(3\tau) \, d\tau[/tex]

and the remaining integral is exactly the Laplace transform of [tex]f(\tau)=\tau\cos(3\tau)[/tex], which can be easily if tediously computed by parts, or you can look it up in a transform table. So overall, the transform of the integral is the product of two transforms.

This is equivalent to the convolution property of the Laplace transform,

[tex]\displaystyle L\left\{f(t) * g(t)\right\} = L\left\{f(t)\right\} L\left\{g(t)\right\}[/tex]

where

[tex]f(t) * g(t) = \displaystyle \int_0^t f(\rho) g(t - \rho) \, d\rho[/tex]

In our case, we let [tex]f(t)=t\cos(3t)[/tex] and [tex]g(t)=g(t-\rho)=1[/tex].

To find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex], we can use the properties of the Laplace transform. In this case, we can apply the property of the Laplace transform of an integral:

[tex]\displaystyle{L\left \{\int_0^t f(t) \, dt \right \} = \dfrac{1}{s} F(s)}[/tex],

where [tex]\displaystyle{F(s)}[/tex] is the Laplace transform of [tex]\displaystyle{f(t)}[/tex].

In this case, [tex]\displaystyle{f(t) = t\cos 3t}[/tex]. Taking the Laplace transform of [tex]\displaystyle{f(t)}[/tex], we have:

[tex]\displaystyle{L\left \{t\cos 3t \right \} = \dfrac{s}{s^2 + 9}}[/tex].

Now, applying the property of the Laplace transform of an integral, we can find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex]:

[tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \} = \dfrac{1}{s} \cdot \dfrac{s}{s^2 + 9} = \dfrac{1}{s^2 + 9} = 1}[/tex].

Therefore, the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex] is 1.

Answer: x = 3.3

Step-by-step explanation:

Based on the given conditions, formulate: 60,000 * 25% * x = 50,000

Multiply the monomials: 15000x = 50,000

Divide both sides of the equation by the coefficient of variable: x = 50,000

                                                                                                                ______

                                                                                                                  15,000

Cross out the common factor: x 10

                                                     3

Round the number: x = 3.3

Answer x = 3.3

The percentage of Americans who have diabetes and the reliability of the diagnostic. The percentage of those who do not have diabetes test negative is 56.8%.

Give that,

The percentage of Americans who have diabetes and the reliability of the diagnostic procedures now in use are listed in the table below.

There are 3 rows in a tables and 4 column.

1st row,

Diabetes---test positive---test negative---total

2nd row,

Have diabetes---36.1%---1.9%---38%

3rd row,

Do not have diabetes---5.2%---56.8%---62%

We have to find the percentage of those who do not have diabetes test negative for the disease.

See the 3rd row,

In that the percentage of those who do not have diabetes test negative is 56.8%.

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Answer:

12.

Step-by-step explanation:

During the previous 3 hours before the New York bus leaves, 6 buses would have left Albany so the New York bus will pass them on the way.

Also 6 buses will leave Albany during the three hours of travel,

Tha answer is 6 + 6 = 12.

The answer to all the subparts are:

So, the formula for mean calculation:

So, we obtain:

The formula for standard error:

So, we get:

[tex]\begin{aligned}&S E=\sqrt{\frac{0.64+(1-0.64)}{50}} \\&S E=\sqrt{0.004608} \\&S E=0.068\end{aligned}[/tex]

So, the standard error is 0.068, and the mean is 32.

Given the size of the sample, a roughly normal shape can be anticipated.

In order to determine the likelihood of scoring less than 60%, we must first determine the z-score using:

So, we obtain:
[tex]\begin{aligned}&z=\frac{0.60-0.64}{0.068} \\&z=-0.588\end{aligned}[/tex]

Then,

Consequently, the probability of receiving a score below 60% is 0.278.

Therefore, the answer to all the subparts are:

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The complete question is given below:
An exam consists of 50 multiple-choice questions. Based on how much you studied, for any given question, you think you have a probability of 0.64 of getting the correct answer. Consider the sampling distribution of the sample proportion of correct questions out of 50. (a) Find the mean and standard error of the sampling distribution of this proportion. Mean = (2 decimal places) Standard error = (3 decimal places) (b) What do you expect for the shape of this sampling distribution? approximately normal because n is large cannot be determined because p is greater than 0.5 cannot be determined because n is large approximately normal because the population is normal (c) If truly p = 0.64, calculate the probability of getting a sample proportion less than 0.60? (correct answers on less than 60% of the questions) Probability = (3 decimal places)

Answer:

p= -8

Step-by-step explanation:

[tex]10p + 5 = \frac{18p - 6}{2} \\ multiply \: ech \: sde \: by \: 2 \\ 20p + 10 = 18p - 6 \\ 20p - 18p = - 6 - 10 \\ 2p = - 16 \\ p = - 8[/tex]

The estimates are used to construct the estimated regression equation:

ŷ = b0 + b1x.

Therefore, the estimates are used to construct the estimated regression equation: ŷ = b0 + b1x.

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The x-intercept of a graph refers to the points where the graph cuts or intersects the x-axis.

These are the x-values when y is equal to zero.

From the graph provided, the values of x when the graph cuts the x-axis are:

Therefore, the coordinates of the x-intercepts are:

The answer type is "Two points".

A mathematical connection known as a function is one in which the values of one or more independent variables determine the values of a single dependent variable. Function implies that the independent variable affects the dependent variable (s).

       The answer is -11

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The complement of the event is diamond, club or spade.

The complement of an event means " to not choose the mentioned one" .

That is in mathematics we define complement as 1 - E, which is also written as E with a bar, here E represents the event.

In this question we would have to pick a card which is complementary to the heart that is the card needs to be a diamond, spade or a club.

Thus the complement of the event is diamond, club or spade.

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Table A matches with x - 3y = 13,  table B matches with 2x - 3y = 9 ,table C matches with 3x -y = -2 and table D matches with 3x - y = -2

What is Linear equation ?

Linear equation can be defined as equation in which highest degree is one.

from the given tables ,

lets first take the values,

x = 0 , y = -4

lets subsitute that in the given equation ,

x - 3y = 12

0 - 3 * -4

= 12

table A matches with equation x - 3y = 13

and subsitute x = 3 and y = - 1

2x - 3y = 9

2*3 - 3* -1

= 9

table B matches with 2x - 3y = 9

put x = -1 and y = 2

3x - y = - 5

3*-1 - 2

= -5

table C matches with 3x -y = -2

put x = -5 y = -13

3x - y = -2

3*-5 - + 13

= -2

table D matches with 3x - y = -2

Therefore, Table A matches with x - 3y = 13,  table B matches with 2x - 3y = 9 ,table C matches with 3x -y = -2 and table D matches with 3x - y = -2

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Step-by-step explanation:

write the question properly