Graph the linear equation. Help 50 points!!

Answer: so there for the answer is 498

Step-by-step explanation:

The quantity of salt in the tank at period t equivalents A(t) = 200 - 130 e(-t/40).

Initially, the tank has A(0) = 50 g of salt.

The rate of salt entryway is (1 g/L) × (5 L/min) = 5 g/min

And a rate of (A(t) ÷ 200 g/L) × (5 L/min) = (A(t) ÷ 40) g/min,

As an outcome, the quantity of salt in the tank modifications as

A'(t) = (5 - A(t)) ÷ 40.

Solve ODE for A(t):

A'(t) + (A(t) ÷ 40) = 4

[tex]e^{\frac{(t)}{40} }[/tex] A'(t) + ([tex]e^{\frac{(t)}{40} }[/tex] ÷ 40 A(t)) = 4[tex]e^{\frac{(t)}{40} }[/tex]

([tex]e^{\frac{(t)}{40} }[/tex] A(t))' = 4[tex]e^{\frac{(t)}{40} }[/tex]

[tex]e^{\frac{(t)}{40} }[/tex] A(t) = 160[tex]e^{\frac{(t)}{40} }[/tex] + C

A(t) = 160 + C[tex]e^{\frac{(t)}{40} }[/tex]

Given A(0) = 30, conclude that

30 = 160 + C

C = -130,

This denotes that the quantity of salt in the tank at period t equivalents

A(t) = 200 - 130 e(-t ÷ 40).

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To determine the percet of shoppers that use coupons, the manager interviews every shopper thay enters the greeting aisle and records wether they use or not coupons.

Since he does not take any measures, nor divide the shopers into groups or, for example, interviews one every k number of shoppers, the sampling method he used is the most simple and common one, named

"Simple random sample" or "random sample"

Answer:

x = 30

Step-by-step explanation:

The sum of the interior angles of a triangle is 180

x + 65 + x + 55 = 180  Combine line terms

2x + 120 = 180  Subtract 120 from both sides

2x = 60  Divide both sides by 2

x = 30

Let's begin by identifying key information given to us:

Principal (p) = $690

Interest rate (r) = 7% = 0.07 per year

Time (t) = 8 years

The amount of money that Ji-yoon has in 8 years is calculated as shown below:

EXPLANATION

The area of the figure can be obtained by applying the following relationship:

Where b=base and height=h

In order to find the height, we need to apply the trigonometric relationship:

Multiplying both sides by 6.4:

Solving the argument:

Switching sides:

Now that we have the height, we can compute the area as follows:

The answer is 53.24 squared inches.

The standard form of the equation of f(x) is option a -x² - 6x + 7

Given,

The graph shows a downward open parabola.

The vertex points are:

(-3, 16), (-7, 0), (1, 0), (-6, 7), (0, 7)

Now,

We have to find the standard form of the function f(x):

As from the graph:

Parabola opens downward, so the function will be negative.

We have the options with:

a = -1, b = -6 and c = 7

Now,

Use x = -b/2a

x = 6/2 × -1 = 6/-2 = -3

Now,

f(x) = -x² - 6x + 7

f(-3) = -(-3)² - 6(-3) + 7

f(-3) = -9 + 18 + 7

f(-3) = 9 + 7

f(-3) = 16

That is, the points for the vertex in this equation is (-3, 16)

Then, the standard form of the equation of f(x) is option a -x² - 6x + 7

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The amount Ali will pay is  £25.80

Define Multiples

A number that can be divided by another number without a remainder.

Multiples of 8 and 12

8 : 8 , 16, 24, 32, 40, 48, 56, 64, 72

12 : 12, 24, 36, 48, 60, 72

common element is 72

72 cakes cost for 12 cakes in each box = 72/12

                                                                 = 6 packs

cost of 6 packs = 6 * £2.50 = £15

72 sausage rolls for 8 sausage in each box = 72 / 8

                                                                       = 9 packs

cost of 9 packs = 9 * £1.20 = £10.80

Total cost will be = £15 +  £10.80 =  £25.80

Hence, the amount Ali will pay is  £25.80

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All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.

In mathematics, a numbered line is a straight line with numbers organized at regular intervals or sections throughout its breadth. The beginning of period is frequently shown laterally and may be shifted in any position.

Anna visited a bowling alley. She did not spend less than or equal to $30, but she did spend more than $25.

The inequality is given as,

$25 < x ≤ $30

All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.

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We will multiply by 26 / 31 in the first number to get second number for fraction in simplest form.

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Given that;

In the fraction,

The first number = 62

The second number = 52

Let the number which can be multiply by the fraction = x

Since, The given condition is,

Multiply the first number by to get the second number.

So, We can formulate;

⇒ 62 × x = 52

Solve for x, as;

⇒ 62 × x = 52

⇒ 62x = 52

Divide by 62, we get;

⇒ x = 52 / 62

Multiply and divide by 2;

⇒ x = 26 / 31

Therefore,

We will multiply by the number 26 / 31 in the first number to get second number for fraction in simplest form.

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The system of quadratic equations obtained on solving general equation of parabola are

a. 5=36a - 6b +c

   -2=64a+8b+c

    3=16a+4b+c

b. 1=289a+17b+c

   -1=81a-9b+c

  2=11025a+105b+c

the equation parabola

the general equation of Parabloa is written as-

y=a[tex]x^{2}[/tex]+bx+c

if the parabola passes through the point. then this point must satisfy the equation of the parabola. so, by putting the value of points we get a set equations-

5=a[tex]6^{2}[/tex]+b(-6)+c

5=36a - 6b +c

and for other two points we get equations

-2=64a+8b+c

and 3=16a+4b+c

and for other three points we get the equations

1=289a+17b+c

-1=81a-9b+c

2=11025a+105b+c

so on solving we get these three set of quadratic equations.

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Answer:

The probability that exactly 4 of them favour the new building project is 0.0768

what is Probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Step-by-step explanation:

We would assume a binomial distribution for the number of people that are in favour of a new building project. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represents the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or samples.

From the information given,

p = 40% = 40/100 = 0.4

q = 1 - p = 1 - 0.4

q = 0.6

n = 5

x = r = 4

Therefore,

P(x = 4) = 5C4 × 0.4^4 × 0.6^(5 - 4)

P(x = 4) = 5 × 0.0256 × 0.6

P(x = 4) = 0.0768

Hence, The probability that exactly 4 of them favour the new building project is 0.0768.

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Using the Pythagorean Theorem, it is found that:

A. The straight line distance between the school and the fire station is of 4.62 miles.

B. The distance between the school and the hospital is of 2.08 miles.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

[tex]h^2 = l_1^2 + l_2^2[/tex]

In the context of this problem, the distance between the school and the fire station is the hypotenuse of a right triangle with sides 4.3 and 1.7, hence:

d² = 4.3² + 1.7²

d = sqrt(4.3² + 1.7²)

d = 4.62 miles.

The hospital is 3.1 miles west of the fire station, hence the distance between the school and the hospital is the hypotenuse of a right triangle of sides 1.7 and 4.3 - 3.1 = 1.2, hence:

d² = 1.2² + 1.7²

d = sqrt(1.2² + 1.7²)

d = 2.08 miles.

The complete problem is given by the image at the end of the answer.

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You can see the three points where the result is equal to an integer in the photo below. Good luck!

Answer:

-88

Step-by-step explanation:

8 x -11 = 88

Answer:

x=15

Step-by-step explanation:

5x+25=100

Subtract 25 from both sides.

5x+25−25=100−25

5x=75

Divide both sides by 5.

5x÷5=75÷5

x=15

[tex]5x+25=100\\x=[/tex]

Subtract 25 from both sides:

[tex]5x+25-25=100-25\\5x=75[/tex]

Divide both sides by 5:

[tex]\frac{5x}{5} =\frac{75}{5}[/tex]

[tex]\fbox{x=15}[/tex]

Answer:

x<-2, x>-7

Step-by-step explanation:

1st one

add 7 to 3 =10

-5 divide by 10 = -2

2nd one

add 7 to -42 = -35

-35 divided by 5 = -7

Angle d is exterior angle . and an exterior angle is equal to addition of two interior angles .

What is the formula for the exterior angle theorem?

In this figure,

       Angle d is exterior angle . and an exterior angle is equal to addition of two interior angles .

So, According to  Exterior Angle Theorem,

                        ∠D = ∠A + ∠B

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Answer:

See explanation below.

Step-by-step explanation:

There is a theorem about the sum of the measures of the angles of a triangle.

In this case, with the interior angle measures called a, b, and c, the theorem states:

Theorem:

The sum of the measures of the interior angles of a triangle is 180°.

a + b + c = 180°

Now we will prove the theorem and answer why a + b = d.

Look at angles c and d. They form a linear pair. Angles that form a linear pair are supplementary angles. By the definition of supplementary angles, the sum of the measures of angles c and d is 180°.

We have

c + d = 180°              Eq. 1

By the theorem above, we have

a + b + c = 180°        Eq. 2

Let's subtract Eq. 1 from Eq. 2:

    a + b + c       = 180°

 -              c + d = 180°

------------------------------

   a + b        - d = 0

a + b - d = 0

Add d to both sides.

a + b = d

That is a proof of the Exterior Angle Theorem.

Answer:

5x-4

Step-by-step explanation:

The equation of the the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5 is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]

Equation of the ellipses:

The Equation of the ellipse with center at (h, k)

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}[/tex]

where,

a = length of semi-major axis

b = length of semi-minor axis

Given,

Here we have the value of center as (1, -3) and the values of a = 7 and b = 5.

Here we need to find the equation of the ellipse.

According to the formula we we have the following values are given,

We know the value of center of ellipses is written as,

(h, k) = (1, -3)

And the values of

a = 7 and b = 5

Therefore, when we apply the values on the formula then we get,

[tex]\frac{(x-1)^2}{7^2}+\frac{(y-(-3))^2}{5^2}[/tex]

When we simplify the term then we get,

[tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]

Therefore, the equation of the ellipse is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex].

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Answer:

either 11 or 21

Step-by-step explanation:

tho I might be 2

Number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy are 16.

Sample timings as observed are 3.5, 3.1, 4.0, 3.5, and 3.9.

Sample-time average (X) = (3.5+3.1+4+3.5+3.9)/5

The average sample time (X) is 3.6.

Observed time (T) Mean (X) (X - T) (X - T)^2

3.5 3.6 0.1 0.01

3.1 3.6 0.5 0.25

4.0 3.6 -0.4 0.16

3.5 3.6 0.1 0.01

3.9 3.6 -0.3 0.09

Allow Standard deviation to be S.

2 in (X-T) - 1 n

[tex]S=\sqrt{\frac{0.52}{4}}[/tex]

S = 0.3605

Considering that (h) = 0.05,

Given that 95% of the time,

Z value at 95% confidence interval = 1.96

Let N be the number of observations.

2 N= Z.S hX

[tex]N=(\frac{1.96X0.3605}{0.05X3.6})[/tex]

N = 15.4

N = 16 (rounded off to next whole number) (rounded off to next whole number)

Consequently, 16 observations are required.

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Answer:

Step-by-step explanation:

Number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy of 16.

Sample-time average (X) = (3.5+3.1+4+3.5+3.9)/5

The average sample time (X) is 3.6. Observed time (T) Mean (X) (XT) (X-T)^2

3.5 3.6 0.1 0.01

3.1 3.6 0.5 0.25

4.0 3.6 -0.4 0.16

3.5 3.6 0.1 0.01

3.9 3.6-0.3 0.09

Allow Standard deviation to be S.

2 in (X-T) - 1n

S=√0.52/4

S=0.3605

Considering that (h) = 0.05,

Given that 95% of the time,

Z value at 95% confidence interval = 1.96 Let N be the number of observations.

2 N=Z.S hx

N=(1.96X0.3605)÷(0.05×3.6)

N = 15.4

N = 16 (rounded off to next whole number) (rounded off to next whole number) Consequently, 16 observations are required.

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Answer: 642 Digits have been used to print 250 Pages

Step-by-step explanation:

A book has 250 pages

1 - 250  Numbers will be used

Single Digit number  -  9   ( 1- 9)

Two Digit Numbers   90  ( 10 - 99)

Three Digit Numbers  151  ( 100 - 250)

Number Of Digits used  = 9 * 1  + 90 * 2  + 151 * 3

= 9 + 180 + 453

= 642

642 Digits have  been used to print 250 Pages

Let's call x to the height. The inequality that represents an acceptable range is:

|x - 35| ≤ 1

Solving it, we get:

x - 35 ≤ 1 or x - 35 ≥ -1

x ≤ 1 + 35 x ≥ -1 + 35

x ≤ 36 x ≥ 34

which is equivalent to 34 ft ≤ x ≤ 36 ft

Answer:

A)  8/15

Step-by-step explanation:

3 / 5 x 8/9

(3/5)(8/9)

(3*8)/(5*9)

(24/45)

8/15

Answer:

8/15

Step-by-step explanation:

3 / 5 x 8/9

Multiplying fractions

Rewriting

3/9 * 8/5

Simplify

1/3 * 8/5

Multiply the numerators

1*8 =8

Multiply the denominators

3*5 = 15

8/15

The eqations are 149=19/9 (10) +b and 130=19/9(1)+b

Given that,

As part of her work, Loren found the solution to the equation 10 = start fraction 19 over 9 end fraction (149) b for b and the points are  (1, 130) and (10, 149)

Finding the slope of a line that goes through two locations for Loren is as follows: m=y2-y1/x2-x1

=149-130/10-1

=19/9 

m=19/9

There are two ways to solve for b in the equation y=mx+b for the location (1,130), where y=130, x=1, and m=19/9, and for the position (10,149), where 149=19/9 (10) +b.

Therefore, the equation of a trend line that passes through the points (1, 130) and (10, 149) are 149=19/9 (10) +b ,130=19/9(1)+b

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