For the rectangle shown, which equation can be used to find the value of x?​

Given:

• Expected number of cans to collect = 24,000 cans.

• The food bank collects 100 fewer cans.

Let's find the number of cans it collected.

Since the food bank collected 100 fewer cans, to find the number of cans it collected, let's subtract 100 from the expected goal which is 24000 cans.

Hence, we have:

Number of cans collected = expected goal - 100

Number of cans collected = 24000 - 100 = 23900

Therefore, the number of cans the food bank collected was 23,900 cans.

ANSWER:

23900 cans

Answer:

C and D are correct.

Step-by-step explanation:

In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

Answer:

C. 8/25 - 19/25i

Step-by-step explanation:

Given that:

\(\dfrac{4-i}{3+4i}\)

\(= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)}\)

\(= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)} \\ \\ =\dfrac{12 -16i -3i+4i^2}{9 - 12i +12i -16i^2} \\ \\ = \dfrac{12-19i+4i^2}{9-16i^2} \\ \\ = \dfrac{8-19i}{25}\)

\(=\dfrac{8}{25}- \dfrac{19i}{25}\)

Answer: B.) 1 and 111 only.

Step-by-step explanation:

75% = 75/100 = 0.75

0.75 falls into the category of rational numbers. Rational numbers comprises of numbers which can be expressed in the form a/b where a and b are integers and B is not 0. Here, both 75 and 100 are integers, thus 75% is a rational number.

Irrational numbers are the opposite of rational numbers thus, 75% is not irrational.

All rational numbers and irrational numbers are REAL numbers, hence, 75% is a real number.

Natural numbers are whole digits starting from 1 e.g ( 1, 2, 3,......). Hence 75% is not a natural number

Whole numbers are natural numbers including 0. (0, 1, 2,.....). Hence, 75% is not a whole number

Integer numbers are comprises of both positive and negative whole numbers. (..., - 1, - 2, 0, 1, 2,...). Hence, 75% is not an integer.

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

The 99.5% confidence interval for the population mean is [74.681, 76.719].

Confidence Interval = (sample mean) ± (critical value) * (standard deviation / √sample size)

Using the given values:

Sample mean  = 75.7

Standard deviation (σ) = 6.8

Sample size (n) = 353

Critical value (z) = 2.807

Confidence Interval = 75.7 ± 2.807 * (6.8 / √353)

In order to calculate the confidence interval accurately to 3 decimal places, we can substitute the values into the equation:

Confidence Interval = 75.7 ± 2.807 * (6.8 / √353)

Confidence Interval = 75.7 ± 2.807 * (6.8 / 18.794)

Confidence Interval = 75.7 ± 2.807 * 0.362

Confidence Interval = 75.7 ± 1.019

Confidence Interval = [74.681, 76.719]

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Answer: C. 3/4 of a cup of corn syrup

Step-by-step explanation:

    We will set up a proportion to help us solve.

\(\displaystyle \frac{1/4\text{ cup corn syrup}}{6\text{ cups of soap and water}} =\frac{x\text{ cups corn syrup}}{18\text{ cups of soap and water}}\)

    Next, we will cross-multiply.

1/4 * 18 = 6 * x

9/2 = 6x

    Lastly, we will divide both sides of the equation by 6.

x = 3/4 of a cup of corn syrup

                       C. 3/4 of a cup of corn syrup

The percentage of drivers who are at least 45 is 62%

From the question, we have the following parameters that can be used in our computation:

The table of values

From the table, we have

Age 45 = 62 percentile

When represented properly

So, we have

Age 45 = 62%

This means that the percentage of drivers who are at least 45 is 62%

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The linear equation for the table and graph is 16x - y + 12 = 0.

Given table:

x                  y

0                 12

2                 44

4                 76

change of y Δy = y2 - y1

Δy = 44 - 12

Δy = 32

change of x Δx = x2 - x1

Δx = 2 - 0

Δx = 2

slope m = Δy/Δx

= 32/2

m = 16

we know that standard line equation is y = mx + c.

substitute (0, 12) and m value we get,

12 = 16(0) + c

c = 12 - 0

c = 12.

substitute c value

y = 16x + 12

16x - y + 12 = 0(which is linear equation)

Therefore the linear equation for the table and graph is 16x - y + 12 = 0.

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Step-by-step explanation:

please subscribe to my mom channel please

Answer:

To solve this problem, we can use the following steps:

Determine the total number of chips produced per minute by all the machines:

Total chips per minute = number of machines * chips per minute per machine

= 90 * 95

= 8,550 chips per minute

Determine the total number of chips produced in one hour:

Total chips per hour = Total chips per minute * number of minutes in an hour

= 8,550 * 60

= 513,000 chips per hour

Determine the total number of chips produced in 5 hours (the time it takes to fill 5 shipping boxes):

Total chips for 5 hours = Total chips per hour * number of hours

= 513,000 * 5

= 2,565,000 chips

Determine the number of chips per shipping box by dividing the total number of chips by the number of shipping boxes:

Chips per box = Total chips / Number of boxes

= 2,565,000 / 5

= 513,000 chips per box

Therefore, there are 513,000 chips per box when 90 machines produce potato chips at a rate of 95 chips per minute.

Answer:

4.75x + 14.40y ≥ 700

Step-by-step explanation:

Given:

Plant cost = $4.75

Shrub cost = $14.40

Number of plant = 80

Number of shrub = 25

Total cost = $700

Find:

Inequality

Computation:

Number of plant = x

Number of shrub = y

4.75x + 14.40y ≥ 700

Answer:

(x+8)^2

Step-by-step explanation:

x^2 +16x+64

What two numbers multiply to 64 and add to 16

8*8 = 64

8+8 = 16

(x+8)(x+8)

(x+8)^2

Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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Answer:

y = 4

Step-by-step explanation:

You are solving for the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction.

Isolate the variable, y. First, subtract 6 from both sides of the equation:

7y + 6 (-6) = 34 (-6)

7y = 34 - 6

7y = 28

Next, divide 7 from both sides:

(7y)/7 = (28)/7

y = 28/7 = 4

y= 4 is one of the equivalent equations that can answer this question.

~

The value of angle x based on the information given is 45°.

Geometry is a branch of mathematics that deals with shapes, angles, dimensions and sizes of different things we see in everyday life

From the image ∠BEC = 160°, ∠FED = 115° and ∠AEF = x°

∠AEC = 180 - 160 = 20° (sum of angles on a straight line)

∠DEB = ∠AEC (vertically opposite angles)

∠DEB = 20°

It should be noted that vertically opposite angles are equal just as denoted above.

x = 180 - ∠DEB - ∠FED  (sum of angles on a straight line)

It should be noted that the sum of angles that are on a straight line is 180°.

x = 180 - 20 - 115

x = 45°

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The slope of the line that passes through the points (0, -6) and (0, -5)is undefined.

Slope is line's inclination with regard to the horizontal is quantified numerically. In analytical geometry, a line, ray, or line segment's slope is the ratio of the vertical to horizontal distance between any two points on the line, ray, or line segment ("slope equals rise over run").

In differential calculus, the derivative of a function yields the slope of a line tangent to its graph, which represents the function's instantaneous rate of change with respect to changes in the independent variable.

Ok so slope is the change in y over change in x.

Your why changed from 6 to -5 so you can write this as -5 - 6

Your x didn’t change it went from 0 to 0

You can write this as 0-0

Now -11/0 is what you end up with as a slope.

Any number divided by 0 is undefined so your slope is undefined.

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Answer:

It is 50,000

Step-by-step explanation:

Because if you were to take the two 2 in front of it would leave you with 57,296, you would know it's 50,000.

Answer:

y=6/7x+11/7

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-5)/(-3-4)

m=-6/-7

m=6/7

y-y1=m(x-x1)

y-5=6/7(x-4)

y=6/7x-24/7+5

y=6/7x-24/7+35/7

y=6/7x+11/7

Answer:

8.54

Step-by-step explanation:

If thousandth's place is ≥ 5 , then add 1 to the hundredth place.

6.487 = 6.49

2.049 = 2.05

6.487 + 2.049 = 6.49 + 2.05  = 8.54

Answer: 0.655

Step-by-step explanation:

Let X be a random variable that represents percent of fat calories that a person in America consumes each day.

As per given , X is normally distributed with a mean \(\mu=36\) and a standard deviation \(\sigma=10\).

Sample size : n= 16

The probability that the average percent of fat calories consumed is more than 35:

\(P(\overline{X}>35)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{35-36}{\dfrac{10}{\sqrt{16}}})\\\\=P(Z>\dfrac{-1}{\dfrac{10}{4}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>\dfrac{-4}{10})\\\\=P(Z>-0.4)\\\\=P(Z<0.4)\ \ \ [P(Z>-z)=P(Z<z)]\\\\=0.655\ \ \ [\text{By p-value table}]\)

Hence, Required probability =0.655

The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = x² - 3

The x-coordinates where the graphs of the equations intersect is when both equations are equal

So, we have

x² - 3 = 2x

Rewrite the equation as

x² - 2x - 3 = 0

When the equation is factored, we have

(x + 1)(x - 3) = 0

So, we have

x = -1 and x = 3

Hence, the x-coordinates are x = -1 and x = 3

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Question

From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

y = 2x

y = x² - 3

Using a t-distribution with 115 degrees of freedom (df = n-1), and a 95% confidence level, we can find the critical value using a t-table or calculator, which is approximately 1.98.

Then, we can calculate the margin of error (ME) using the formula:

ME = critical value x standard error

where the standard error (SE) is given by:

SE = standard deviation / sqrt(sample size)

Substituting the given values, we get:

SE = 30 / sqrt(116) ≈ 2.78

ME = 1.98 x 2.78 ≈ 5.5

Finally, we can construct the 95% confidence interval (CI) for the mean weight using the formula:

CI = sample mean ± margin of error

Substituting the given values, we get:

CI = 177 ± 5.5

CI ≈ [171.5, 182.5]

Therefore, the 95% confidence interval for the mean weight of the residents in the town is approximately [171.5, 182.5] pounds.

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Answer:

It is 50000 sq. Yards.

Hope it helps

Trains make up approximately 49.04% of the total journeys across all modes of transportation.

We must divide the total number of train trips by the total number of trips made using all modes of transportation, then multiply the result by 100 to get the percentage that trains make up of the total.

There have been 2320 train trips overall, and there have been 4730 trips overall using all forms of transportation.

Trains therefore account for the following proportion of the total:

(2320 / 4730) x 100% = 49.04%

Train travel thus accounts for roughly 49.04 percent of all travels made using all modes of transportation.

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(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

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9514 1404 393

Answer:

  A)  B = 37.2°, b = 309.1, c = 382.3

Step-by-step explanation:

You know the third angle must be ...

  B = 180° -131.6° -11.2°

  B = 37.2° . . . . . . eliminates choice D

You know the two missing sides are both longer than 99.3, eliminating choice C.

Since angle C is the largest angle, side c is the longest side, eliminating choice B.

By the process of elimination, we know the correct choice is A.

__

The Law of Sines will tell you the length of side C is related to the other triangle values by ...

  c/sin(C) = a/sin(A)

  c = (99.3 ft)×sin(131.6°)/sin(11.2°)

  c ≈ 382.3 ft . . . . matches choice A

Given:

Simplify the fraction,

Answer:

Complete Question

The  complete question is shown on the first uploaded image  

Answer:

The interval is  \(-0.0037 < p_1-p_2<-0.0023\)

Step-by-step explanation:

From the question we are told that

   The first  sample size is  \(n _1 = 1068000\)

    The  first sample proportion is \(\r p_1 = 0.089\)

    The  second sample  size is  \(n_2 = 1476000\)

    The  second sample proportion is  \(\r p_2 = 0.092\)

Given that the confidence level is  95% then the level of significance is mathematically evaluated as

             \(\alpha = (100 - 95 )\%\)

              \(\alpha = 0.05\)

Next we obtain the critical value  of  \(\frac{\alpha }{2}\)  from the normal distribution table  

The value is  

               \(Z_{\frac{\alpha }{2} } =z_c= 1.96\)

Generally the 95% confidence interval is mathematically represented as

       \((\r p_1 - \r p_2 ) -z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}} < (p_1 - p_2 ) < (\r p_1 - \r p_2 ) +z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}}\)

Here  \(\r q_1\) is mathematically evaluated as \(\r q_1 = (1 - \r p_1)= 1-0.089 =0.911\)

and  \(\r q_2\)  is mathematically evaluated as  \(\r q_2 = (1 - \r p_2) = 1- 0.092 = 0.908\)

So

       \((0.089 - 0.092 ) -1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}} < (p_1 - p_2 ) < (0.089 - 0.092 ) +1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}}\)

\(-0.0037 < p_1-p_2<-0.0023\)