Caleb went to the grocery store and purchased cans of soup and frozen
dinners. Each can of soup has 200 mg of sodium and each frozen dinner has
500 mg of sodium. Caleb purchased a total of 15 cans of soup and frozen
dinners which collectively contain 4500 mg of sodium. Determine the
number of cans of soup purchased and the number of frozen dinners
purchased.

The formula for the centripetal force, as a function of the radius, is given as follows:

F = 896/r.

The equation that defines a direct proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse proportional relationship, the equation is given as follows:

y = k/x.

The centripetal force varies inversely with the radius, hence the equation is given as follows:

F = k/r.

When F = 56, r = 16, hence the constant k is obtained as follows:

56 = k/16

k = 56 x 16

k = 896.

Hence the equation is given as follows:

F = 896/r.

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SOLUTION

Write out the expression given;

To simplify this expression, we set put the expression as given in the image below.

Therefore

Answer; 12. 025

Answer:

\(115 \dfrac{1}{2}\:cm^3\)

Step-by-step explanation:

The volume of a rectangular prism is the product of each of the sides of the prism

Given the sides have lengths
\(3\dfrac{1}{2}, 6 \;and\; 5 \dfrac{1}{2} cm\)

the volume would be
\(3\dfrac{1}{2} \times 6 \times 5 \dfrac{1}{2}\)

To perform this multiplication, convert mixed fractions to improper fractions first

Use the rule that mixed fraction
\(a\dfrac{b}{c}=\dfrac{a\times \:c+b}{c}\)

\(3\dfrac{1}{2}=\dfrac{3\times 2+1}{2} = \dfrac{7}{2}\)

\(5\dfrac{1}{2}=\dfrac{5\times 2+1}{2}= \dfrac{11}{2}\)

Therefore
\(3\dfrac{1}{2}\times \:6\times \:5\dfrac{1}{2}\\\\= \dfrac{7}{2}\times \:6\times \dfrac{11}{2}\\\\= \dfrac{7}{2}\times \dfrac{6}{1}\times \dfrac{11}{2} \quad(6 = \dfrac{6}{1})\)

\(=\dfrac{7\times \:6\times \:11}{2\times \:1\times \:2}\\\\= \dfrac{462}{4}\\\)

Divide numerator and denominator by 2 to get
\(\dfrac{231}{2}\\\)

Convert improper fraction \(\dfrac{231}{2}\) to mixed fraction using quotient/remainder

\(\dfrac{231}{2} \\\\\rightarrow Quotient: 115\\\\\rightarrow Remainder = 231 - 115 \times 2 = 231 - 230 = 1\)

\(\dfrac{231}{2} = 115 \dfrac{1}{2}\)

Answer:

If your weekly allowance is 5, then for Christmas week your allowance was 15, then your allowance went up by: 5 =3 - 1 = 2 x 100 =200%.

Answer:

you cannot not have a percentage greater than 100

Step-by-step explanation:

I do

not know

I believe that it is 2x^2+1x-2

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is: ∠A = 39.6°

3) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

3) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

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Answer:-39

Step-by-step explanation:

The first thing is to open the bracket.

By doing that, the question becomes -37-2.

note that plus×minus=minus.

Hence,-39 as the final answer

Hence, we know that area of rectangle is equals to the product of length and breadth.

Therefore, the area of rectangle is,

\( = 4 \times( {x}^{2} +3x + 2 ) \\ = 4({x}^{2} + 3x + 2) \\ = \green{ \boxed{4 {x}^{2} + 12x + 8}}\)

Therefore, the answer is 4x² + 12x + 8.

Step-by-step explanation:

Find equation of the parabola to be   - 1/4 ( x-3)^2 -1

  expanded this =      y=   - 1/4 x^2 + 6/4 x- 13/4

           derivative of this is        - 1/2 x + 6/4

                 set this equal to the desired slope (1/2)

                              - 1/2 x + 6/4 = 1/2

                                 - 1/2 x = -1

                                        x = 2

Perimeter of the given polygon is 16.94 units.

To measure the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the ex[pression,

Distance = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

By using this expression,

Distance between A(0, 4) and B(2, 0) = \(\sqrt{(0-2)^2+(4-0)^2}\)

                                                              = \(\sqrt{20}\) units

Distance between B(2, 0) and C(2, -2) = \(\sqrt{(2-2)^2+(0+2)^2}\)

                                                               = 2 units

Distance between C(2, -2) and D(0, -2) = \(\sqrt{(0-2)^2+(-2+2)^2}\)

                                                                 = 2 units

Distance between D(0 -2) and E(-2, 2) = \(\sqrt{(0+2)^2+(-2-2)^2}\)

                                                                = \(\sqrt{20}\) units

Distance between E(-2, 2) and F(-2, 4) = \(\sqrt{(-2+2)^2+(2-4)^2}\)

                                                               = 2 units

Distance between F(-2, 4) and A(0, 4) = \(\sqrt{(-2-0)^2+(4-4)^2}\)

                                                               = 2 units

Perimeter of ABCDEF = AB + BC + CD + DE + EF + FA

                                     = \(\sqrt{20}+2+2+\sqrt{20}+2+2\)

                                     = \(8+2\sqrt{20}\)

                                     = 16.94 units

      Therefore, perimeter of the given polygon in the graph attached is 16.94 units.

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Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

Answer:

60°

Step-by-step explanation:

In similar triangles, the corresponding angles are congruent.

          ∠O = R

          O = 70°

In ΔOMN,

      ∠O + ∠M + ∠N = 180     {Angle sum property of triangle}

       70 + 50 + Ф    = 180

               120 + Ф  = 180

Subtract 120 from both sides,

                        Ф  = 180 - 120

                         Ф = 60°  

Answer:

41.93 degrees

Step-by-step explanation:

Answer:

4 candy bars cost $5.16?

Step-by-step explanation:

I just added it 4 four times.

Answer:

C= $1.29n

Step-by-step explanation:

Using the knowledge of the measure of a semicircle, the measures in the circle given are:

a. m(DEF) = 152°

b. m(EFG) = 70°

c. m(CA) = 28°

Half of a circle is a semicircle = 180°.

Given the following:

a. m(DEF) = [m(CDE) - m(DC)] + [m(EF)]

m(DEF) = (152 - 39) + 39

m(DEF) = 152°

b. m(EFG) = m(EF) + m(FG)

m(EFG) = 39 + 31 = 70°

c. m(CA) = 180 - 152 (semicircle)

m(CA) = 28°

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Answer:

b-a=60-50

Step-by-step explanation:

6% is $ 192.00 of 3200.00.

Let x be the percentage.

x = 192 * 100 / 3200

= 19200/3200

= 192/32

x = 6%.

Therefore 6% is $ 192.00 of 3200.00.

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he two numbers that multiply to -35 and add to get -18 are -5 and 3.

To see why, you can use the factoring method. First, find two numbers that multiply to give you -35. The factors of -35 are -1, 1, -5, and 5. So, the two numbers that multiply to -35 are either -5 and 7 or 5 and -7.

Next, find which pair of numbers adds up to -18. It's clear that 5 and -7 add up to -2, so they don't work. However, if we choose -5 and 3, we get:

-5 + 3 = -2

So, -5 and 3 are the two numbers that multiply to -35 and add to -18.

We can be 90% confident that the interval [76.4, 79.3] contains the true mean monthly percentage of on-time departures. This means that we are highly confident that the true mean monthly percentage of on-time departures lies within this interval.

To find the 90% confidence interval, we first need to calculate the margin of error. To calculate this, we need to use the standard error, which is calculated by dividing the standard deviation by the square root of the sample size. The standard deviation for the given data is 2.2 and the sample size is 72 (6 years × 12 months). So, the standard error is calculated as 2.2/√72 = 0.44. The margin of error is then calculated by multiplying the standard error by the critical value for 90% confidence, which is 1.645. The margin of error is therefore 0.44 × 1.645 = 0.72. The confidence interval is then calculated by adding and subtracting the margin of error from the sample mean. The sample mean is 77.8, so the 90% confidence interval is 77.8 ± 0.72, or [76.4, 79.3]. This means that we are highly confident that the true mean monthly percentage of on-time departures lies within this interval.

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Answer:

x = -7/2

x = 5

Step-by-step explanation:

Answer:

(2x+7)(x-5)=0

2x+7=x-5

2x-x=5-7

X=-2

Answer:

JL = 21

Step-by-step explanation:

Given that K is on line segment JL, therefore:

KL + JK = JL (according to segment addition postulate)

KL = 2x - 2

JK = 5x + 2

JL = 4x + 9

Thus:

\( (2x - 2) + (5x + 2) = (4x + 9) \)

Solve for x

\( 2x - 2 + 5x + 2 = 4x + 9 \)

\( 2x +5x - 2 + 2 = 4x + 9 \)

\( 7x = 4x + 9 \)

Subtract 4x from both sides

\( 7x - 4x = 4x + 9 - 4x \)

\( 3x = 9 \)

Divide both sides by 3

\( \frac{3x}{3} = \frac{9}{3} \)

\( x = 3 \)

Find the numerical length of JL

\( JL = 4x + 9 \)

Plug in the value of x

\( JL = 4(3) + 9 = 12 + 9 = 21 \)

Answer:

\(\huge\boxed{\sf <x = 24\°}\)

Step-by-step explanation:

∠x and 156° are supplementary i.e. angles on a straight line that add up to 180 degrees.

So,

∠x + 156 = 180

Subtract 156 to both sides

∠x = 180 - 156

∠x = 24°

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

\(\boxed{\sf x=24\°}\)

Step-by-step explanation:

From the given diagram, we can see that ∠BOC and ∠AOB are supplementary angles.

Therefore, \(\sf m=\angle BOC+m\angle AOB=180\°\)

\(\sf m=\angle BOC+m\angle AOB=180\°\)

\(\sf x+156=180\°\)

Subtract 156 from both sides:

\(\sf x+156-156=180-156\)

\(\sf x=24\°\)

__________________________________

Answer:

85

Step-by-step explanation:

From the question given above, the following data were obtained:

Ratios of the angle => 2 : 4 : 5 : 6

Difference between the largest angle and the smallest angle​ =?

Next, we shall determine the various angles in the quadrilateral. This can be obtained as follow:

Ratios of the angle => 2 : 4 : 5 : 6

Total ratio = 2 + 4 + 5 + 6

Total ratio = 17

Angle in a quadrilateral = 360

For ratio 2:

Angle = 2/17 × 360 ≈ 42

For ratio 4:

Angle = 4/17 × 360 ≈ 85

For ratio 5:

Angle = 5/17 × 360 ≈ 106

For ratio 6:

Angle = 6/17 × 360 ≈ 127

SUMMARY:

The angles are => 42°, 85°, 106° and 127°

Finally, we shall determine the difference between largest angle and the smallest angle​. This can be obtained as follow:

Smallest angle = 42°

Largest angle = 127°

Difference between the largest angle and the smallest angle​ =?

Difference = Largest – Smallest

Difference = 127 – 42

Difference = 85

Thus, the difference between the largest angle and the smallest angle​ is 85.

Answer:

X = 66

Step-by-step explanation:

A straight line is equal to 180 degrees so if you have one side of that line you can figure out the inside angle.

Now that you have two of the angles inside the triangle add them up. All the interior angles of a triangle will add to 180. So add up 38 and 76 to get 114. Now do 180 - 114, you should get 66

so x = 66

Complete Question

A person standing 213 feet from the base of a church observed the angle of elevation to the church's steeple to be 33 ∘. Find the height of the church

Answer:

138.3 ft

Step-by-step explanation:

We solve this question above using using the Trigonometric function of Tangent.

tan θ = Opposite/Adjacent

Where:

Opposite = Height of the church = x

Adjacent = Distance for the base of the church = 213ft

Angle of elevation θ = 33°

Hence:

tan 33 = x /213 ft

Cross Multiply

x = tan 33 × 213 ft

x = 138.32381735 ft

x = Opposite Approximately = 138.3 ft

Therefore, the height of the church = 138.3 ft

The mean is  2,071,798.33

The Median is 1,485,552

The range is 7,425,310

The standard deviation is given as 1961105.68

Mean = (Sum of all populations) / (Number of cities)

= (8,336,817 + 979,576 + 2,693,976 + 2,320,268 + 1,680,992 + 1,584,064 + 1,547,253 + 1,423,851 + 1,343,573 + 1,021,795 + 978,908 + 911,507) / 12

= 24,861,580 / 12

= 2,071,798.33

To find the median, we need to arrange the populations in increasing order and find the middle value. If we arrange these values, we get:

911,507, 978,908, 979,576, 1,021,795, 1,343,573, 1,423,851, 1,547,253, 1,584,064, 1,680,992, 2,320,268, 2,693,976, 8,336,817

Since there are 12 cities (an even number), the median would be the average of the 6th and 7th values:

Median = (1,423,851 + 1,547,253) / 2

= 1,485,552

The mode isn't applicable here as no city population repeats.

The range is the highest population minus the lowest population:

Range = 8,336,817 - 911,507

= 7,425,310

Standard deviation  =  (911507- 2068548.3333333)² +  (978908 - 2068548.3333333)² + (979576  - 2068548.3333333)²  + ( 1021795 -  2068548.3333333)² +  (1343573- 2068548.3333333)²  +( 1423851- 2068548.3333333)² + (1547253- 2068548.3333333)² +( 1584064- 2068548.3333333)² + (1680992- 2068548.3333333)² + ( 2320268- 2068548.3333333)²  +(2693976- 2068548.3333333)² +( 8336817 - 2068548.3333333)² / 12

= 46151226311869 / 12

=  3845935525989.1

\(standard deviation = \sqrt{ 3845935525989.1}\)

=  1961105.6896529

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The probability that more than 240 flights in a random sample of 400 commercial airline flights will arrive on time is approximately 1 or 100%.

To solve this problem using a normal approximation, we need to calculate the mean (μ) and standard deviation (σ) of the binomial distribution and then use the normal distribution to approximate the probability.

Given:

Probability of an airline flight arriving on time (success): p = 0.84

Number of trials (flights): n = 400

Number of flights arriving on time (successes): x > 240

First, we calculate the mean and standard deviation of the binomial distribution using the following formulas:

Mean (μ) = n * p

Standard Deviation (σ) = √(n * p * (1 - p))

μ = 400 * 0.84 = 336

σ = √(400 * 0.84 * 0.16) = √(53.76) ≈ 7.33

Now, we can use the normal distribution to find the probability that more than 240 flights will arrive on time. Since we're interested in the probability of x > 240, we will calculate the probability of x ≥ 241 and then subtract it from 1.

To use the normal distribution, we need to standardize the value of 240:

z = (x - μ) / σ

z = (240 - 336) / 7.33

z ≈ -13.13

Now, we can find the probability using the standard normal distribution table or a calculator. Since the value of z is extremely low, we can approximate it as:

P(x > 240) ≈ P(z > -13.13)

From the standard normal distribution table or calculator, we find that P(z > -13.13) is essentially 1 (close to 100%).

Therefore, the probability that more than 240 flights in a random sample of 400 commercial airline flights will arrive on time is approximately 1 or 100%.

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Answer:

a)  The joint probability distribution

P(0,0) = 0.36, P(1,0) = 0.24,   P(2,0) = 0,   P(0,1) = 0,  P(1,1) = 0.24,  P(2,1)= 0.16

b)  P( W = 0 ) = 0.36,    P(W = 1 ) = 0.48,  P(W = 2 ) = 0.16

c) P ( z = 0 ) = 0.6

  P ( z = 1 ) = 0.4

Step-by-step explanation:

Number of head on first toss = Z

Total Number of heads on 2 tosses = W

% of head occurring = 40%

% of tail occurring = 60%

P ( head ) = 2/5 ,    P( tail ) = 3/5

a) Determine the joint probability distribution of W and Z

P( W =0 |Z = 0 ) = 0.6         P( W = 0 | Z = 1 ) = 0

P( W = 1 | Z = 0 ) = 0.4        P( W = 1 | Z = 1 ) = 0.6

P( W = 1 | Z = 0 ) = 0           P( W = 2 | Z = 1 ) = 0.4

The joint probability distribution

P(0,0) = 0.36, P(1,0) = 0.24,   P(2,0) = 0,   P(0,1) = 0,  P(1,1) = 0.24,  P(2,1)= 0.16

B) Marginal distribution of W

P( W = 0 ) = 0.36,    P(W = 1 ) = 0.48,  P(W = 2 ) = 0.16

C) Marginal distribution of Z ( pmf of Z )

P ( z = 0 ) = 0.6

P ( z = 1 ) = 0.4

Part(a): The required joint probability of W and Z is ,

\(P(0,0)=0.36,P(1,0)=0.24,P(2,0)=0,P(0,1)=0,P(1,1)=0.24,\\\\P(2,1)=0.16\)

Part(b): The pmf (marginal distribution) of W is,

\(P(w=0)=0.36,P(w=1)=0.48,P(w=2)=0.16\)

Part(c): The pmf (marginal distribution) of Z is,

\(P(z=0)=0.6,P(z=1)=0.4\)

Part(a):

The joint distribution is,

\(P(w=0\z=0)=0.6,P(w=1|z=0)=0.4,P(w=2|z=0)=0\)

Also,

\(P(w=0\z=1)=0,P(w=1|z=1)=0.6,P(w=2|z=1)=0.4\)

Therefore,

\(P(0,0)=0.36,P(1,0)=0.24,P(2,0)=0,P(0,1)=0,P(1,1)=0.24,\\\\P(2,1)=0.16\)

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