Samuel went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 300 mg of sodium and each frozen dinner has 450 mg of sodium. Samuel purchased 5 more frozen dinners than cans of soup and they all collectively contain 6000 mg of sodium. Write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. Define the variables that you use to write the system.

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To close the expansionary gap, the government would need to decrease spending by $100 billion.

The formula to calculate the change in equilibrium output due to a change in government spending is:

∆Y = (∆G / (1 - MPC))

Where:

∆Y = change in equilibrium output

∆G = change in government spending

MPC = marginal propensity to consume

Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).

Given that MPC = 3/4, we can plug in the values into the formula:

400 = (∆G / (1 - 3/4))

∆G = (1 - 3/4) * 400

∆G = (1/4) * 400

∆G = 100

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To know more about interest rate visit:

https://brainly.com/question/14445709

#SPJ1

Answer:

[tex]10 = -4( - 1) + b[/tex]

[tex]10 = 4 + b[/tex]

[tex]b = 6[/tex]

[tex]y = - 4x + 6[/tex]

The equation of the line in slope-intercept form is y = -4x + 6.

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

Given that the slope is -4 and the line passes through the point (-1, 10), we can substitute these values into the equation.

Using the point-slope formula (y - y1) = m(x - x1), we can rewrite it as (y - 10) = -4(x - (-1)). Simplifying this equation, we get y - 10 = -4x - 4, and rearranging it, we have y = -4x + 6. Therefore, the equation of the line in slope-intercept form is y = -4x + 6.

https://brainly.com/question/33578579

#SPJ3

Answer:

Let m be the mass of the object and w be the weight of the object. According to the problem, weight varies directly with mass, so we can write:

w = k * m

where k is the constant of proportionality.

To find k, we can use the information given in the problem. We know that when m = 2 kg, w = 4 N. Substituting these values into the equation above, we get:

4 N = k * 2 kg

Solving for k, we get:

k = 4 N / 2 kg = 2 N/kg

Now we can use this value of k to find the mass of an object that weighs 18 N. We can rearrange the equation above to solve for m:

m = w / k

Substituting w = 18 N and k = 2 N/kg, we get:

m = 18 N / 2 N/kg = 9 kg

Therefore, the mass of the object that weighs 18 N is 9 kg.

Answer: 3/4

Step-by-step explanation:

Any number as the denominator of the fraction that is less than 8 (the denominator) will give you a fraction greater than 3/8.

Another different answer could be 3/5 or 3/6.

A fraction that has a value greater than 3/8 using 3 as the numerator is 3/6, 3/4, 3/2 and so on.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

The given fraction is 3/8.

Here, 3/8 = 0.375

We need write the fraction which is greater than 3/8 using 3 as the numerator is 3/6 = 0.5

Therefore, a fraction that has a value greater than 3/8 using 3 as the numerator is 3/6, 3/4, 3/2 and so on.

To learn more about the fraction visit:

brainly.com/question/1301963.

#SPJ2

Answer:

Step-by-step explanation:

BD is craxking treys and cracking treys is gd dissing bd you can look it up i ffrom o block and bd is the opps im telling so you wont lose yo life so please play right if you gdk be gdk if u gd be gd we aint bd ofn

Check the picture below.

[tex]\sin(38^o )=\cfrac{\stackrel{opposite}{x}}{\underset{hypotenuse}{7}}\implies 7\sin(38^o)=x\implies 4.31\approx x \\\\[-0.35em] ~\dotfill\\\\ \cos(38^o )=\cfrac{\stackrel{adjacent}{y}}{\underset{hypotenuse}{7}}\implies 7\cos(38^o)=y\implies 5.52\approx y[/tex]

Make sure your calculator is in Degree mode.

Answer:

Step-by-step explanation:

You want the leg measures in a right triangle with a hypotenuse of 7 inches and an angle of 38°.

The mnemonic SOH CAH TOA reminds you of the relations between side lengths and trig functions:

  Sin = Opposite/Hypotenuse   ⇒   Opposite = Hypotenuse×Sin

  Cos = Adjacent/Hypotenuse   ⇒   Adjacent = Hypotenuse×Cos

The given triangle will have opposite and adjacent sides of ...

  opposite = (7 in)sin(38°) ≈ 4.31 in

  adjacent = (7 in)cos(38°) = 5.52 in

The leg lengths of the triangle are 4.31 inches and 5.52 inches.

Answer:

16.77 cm²

Step-by-step explanation:

Area of rectangle = L x W

L = 4.3 cm

Width = 3.9 cm

Let' solve

4.3 x 3.9 = 16.77 cm²

So, the area of the rectangle is 16.77 cm²

Answer: To solve this problem, we can use the binomial distribution formula. Let X be the number of blue jelly beans in a bag of 200 jelly beans. Then X follows a binomial distribution with parameters n = 200 and p = 0.15, where p is the probability of drawing a blue jelly bean.

The probability of getting more than 20% blue jelly beans in a bag can be calculated as:

P(X > 0.2*200) = P(X > 40)

We can use the normal approximation to the binomial distribution, since n is large (200) and p is not too close to 0 or 1. Using the mean and variance of the binomial distribution, we can calculate the corresponding mean and standard deviation of the normal distribution as follows:

μ = np = 200 * 0.15 = 30

σ = sqrt(np(1-p)) = sqrt(200 * 0.15 * (1-0.15)) = 4.07

Then, we can standardize the random variable X as:

Z = (X - μ) / σ

So, we have:

P(X > 40) = P((X - μ) / σ > (40 - μ) / σ)

= P(Z > (40 - 30) / 4.07)

= P(Z > 2.46)

Using a standard normal distribution table or a calculator, we find that P(Z > 2.46) is approximately 0.007. Therefore, the probability that a bag will contain more than 20% blue jelly beans is about 0.007 or 0.7%.

Step-by-step explanation:

Average Minutes Per Night Spent On Homework

0 20

48 60

190

Average Minutes Per Night Spent Watching TV

0 10

20 30

50

11. What is the median for TV time?

12. What is the range of times that the middle 50% of the sophomores spend on TV per night?

13. What percent of the sophomores spend more than 30 minutes per night watc

Answer: To find the P-value, we first need to determine the direction of the alternative hypothesis. Since the alternative hypothesis is two-tailed, we need to divide the significance level (α) by 2 before finding the critical values and the rejection region. Therefore, we have:

H0: p = 0.06

Ha: p ≠ 0.06

α = 0.05/2 = 0.025

The test statistic is z = 1.79, which represents the number of standard errors that the sample proportion is from the hypothesized population proportion under the null hypothesis. We can find the P-value by looking up the area in the standard normal distribution table beyond the test statistic in both tails:

P-value = P(Z ≤ -1.79 or Z ≥ 1.79)

= P(Z ≤ -1.79) + P(Z ≥ 1.79)

= 0.0364 + 0.0364

= 0.0728

Therefore, the approximate P-value for Elliot's significance test is 0.0728. Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion of adults who bike to work in Elliot's city has changed significantly from the previous year.

Step-by-step explanation:

Jackson is on point. Of all fish, catfish make up one-third of the total.

The United States of America, Great Britain, and other English-speaking countries predominately utilise the pound as a unit of weight.

Any quantity associated with something is assumed to contain one pound if it does. The pound is the most widely used weight unit in the English-speaking world, including Britain, America, and other nations.

Zebra danios make up half of all the fish.

More fancy guppies than catfish, by a factor of two.

x = guppies

2x = catfish

x + 2x = 1/2 of the fish population

3x = 1/2 of the fish population

3x * 2 = 6x

x = 1/6 number of fancy guppies

catfish:

2x = 2(1/6) = 2/6 = 1/3 catfish.

Jackson is on point. Of all fish, catfish make up one-third of the total.

To know more about pounds, visit:

brainly.com/question/498964

#SPJ1

The complete question is,

Alberto puts 3 kinds of fish in his fish tank: zebra danios, fancy guppies, and cat fish. Half of Alberto's fish are zebra danios. He has 2 times as many catfish as he has fancy guppies. Alberto's friend Jackson says 1/3 of Alberto's fish are catfish. Is Jackson correct?

Answer:

$526.75 i believe

Step-by-step explanation:

The range of the relation whose graph is shown include the following: C. -1 ≤ y ≤ 1.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-4, 4} or -4 ≤ x ≤ 4.

Range = {-1, 1} or -1 ≤ y ≤ 1.

Read more on domain here: brainly.com/question/17440903

#SPJ1

Answer: To find the circumference of a circle, there are 2 formulas.

Step-by-step explanation:

The first formula is 2πr and the second formula is πd when solving any math problem. You can use either one but you would use which one is the most helpful to answer your question. Hope this helps!

Answer:5

Step-by-step explanation: hope this helps

Answer:  1st one

Step-by-step explanation:

The measure of  angle CFE is determined as 29⁰.

The measure of angle CFE is calculated by applying the following formula.

The intersecting chord theorem, also known as the intersecting chords inside and outside theorem, is a geometric property that applies to chords (line segments that connect two points on the circumference of a circle) that intersect inside or outside a circle.

Based on the angle of intersecting chord theorem, we will have the following equation.

m∠CFE = ¹/₂( arc angle CE )

arc CE = 360 - 302 (sum of angles in a circle)

arc CE = 58⁰

m∠CFE = ¹/₂ x 58

m∠CFE = 29⁰

Learn more about chord angles here: brainly.com/question/23732231

#SPJ1

The discount allowed for a cash payment of GH 5,600.00 is given as follows:

GHC 280.00.

The discount allowed for a cash payment of GH 5,600.00 is obtained applying the proportions in the context of the problem.

There is a 5% discount, hence the value of the discount is obtained as follows:

0.05 x 5600 = GHC 280.00.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

The amount of persons who have heard in 30mins would be:

45 persons

The initial mass (in mg) of the sample is  32 mg

The mass 7 weeks after the start is 0.198 mg

Exponential decay is a process in which a quantity decreases at a rate proportional to its value. This means that the larger the quantity, the faster it will decrease.

Exponential decay is modeled by the following formula:

[tex]A = A_{0} \times (1/2)^{\frac{t}{T} }[/tex]

where A is the amount after time t, A₀ is the initial amount,

T is the half-life, and t is the time elapsed

Here we have

The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.

For the first question, we know that after 16 days, the amount is 2 mg, and the half-life is 4 days. We can plug these values into the formula:

[tex]2 = A_{0} \times (1/2)^{\frac{16}{4}}[/tex]

Simplifying, we get:

2 = A₀ × (1/2)⁴

2 = A₀ × (1/16)

A₀ = 2 × 16

A₀ = 32 mg

So the initial mass of the sample was 32 mg.

For the second question, we need to find the mass after 7 weeks, or 49 days. We can use the same formula, but with t = 49:

[tex]A = 32 \times (1/2)^{\frac{49}{4} }[/tex]

A ≈ 0.198 mg

Therefore,

The initial mass (in mg) of the sample is  32 mg

The mass 7 weeks after the start is 0.198 mg

Learn more about Exponential decay at

https://brainly.com/question/2193799

#SPJ1

Both Jeremy and Aksa could be right, depending on how they are counting the cubes for finding the volume of a prism.

A prism is a three-dimensional solid shape with a constant cross-section, usually a polygon. It is characterized by two identical end faces, parallel and congruent bases, and straight lateral faces connecting the bases.

Both Jeremy and Aksa could be right, depending on how they are counting the cubes.

If the prism has a square base with 4 cubes along each side, then there would be 16 cubes in each layer. If there are 4 layers, then the total volume would be 16 x 4 = 64 cubic units.

However, if the prism has a rectangular base with 6 cubes along one side and 4 cubes along the other side, then there would be 24 cubes in each layer. If there are 4 layers, then the total volume would be 24 x 4 = 96 cubic units.

Therefore, the answer depends on the shape of the prism and how the layers are counted.

To know more about Prism visit:

https://brainly.com/question/23963432

#SPJ1

Answer:

all numbers greater than 8

Step-by-step explanation:

simply pick any number greater than 8, since the > symbol is in front of 8. By the way, you cannot pick 8. :) I hope this helps!

On the x-axis use a scale of 2 units for each grid square. on the y-axis use a scale of 10 units of each grid square. The x-coordinates range from -5 to 5. y-coordinates range from -40 to 50.

In mathematics, points and functions are represented and graphed on the coordinate plane, commonly known as the Cartesian plane. The x-axis and y-axis are two perpendicular number lines that meet at the origin to form the plane (0,0).

On the coordinate plane, points are denoted by ordered pairs (x, y), where x denotes the point's separation from the y-axis and y denotes its separation from the x-axis.

For the given coordinates the range of x and y coordinates are:

x-coordinates range from -5 to 5

y-coordinates range from -40 to 50.

Thus, we use a scale of 2 on the x-axis and 10 units on the y axis.

Learn more about coordinate plane here:

https://brainly.com/question/24134413

#SPJ1

The investment will be worth approximately $4468 after 14 years.

Annual interest rate is the rate at which an investment or loan grows in value over the course of a year, expressed as a percentage. It represents the cost of borrowing or the return on investment over one year.

The following equation can be used to determine the future value of an investment using compound interest:

FV = P * (r/n + 1)(n*t)

Where:

FV is the investment's future value.

The principal is P. (initial investment)

The annual interest rate is represented by r,

The number of times the interest is compounded annually by n (expressed as a decimal).

t is the time (in years)

In this case:

P = $1500

r = 8.5% = 0.085

n = 1 (compounded annually)

t = 14

With these values entered into the formula, we obtain:

FV = 1500 * [tex](1 + 0.085/1)^(1*14)[/tex]

     = $4467.56

Therefore, the investment will be worth approximately $4468 after 14 years.

To know more about annual interest rate visit:

https://brainly.com/question/30573341

#SPJ1

Answer:Let's assume the number of haircuts Hayley needs to perform in a month for the total amount paid to either salon to be the same is denoted as 'x'.

For self-employment at The Princeton Salon:

Hayley would pay a fixed monthly rent of $774 to rent a station and keep all of her earnings.

For working at a franchise:

Hayley would have to pay $9 to the salon for every haircut she performs.

Based on the given information, we can set up the following equation to find the value of 'x':

Number of haircuts * Cost per haircut at franchise = Monthly rent at The Princeton Salon

x * 9 = 774

Solving for 'x':

x = 774/9

x ≈ 86.00

So, Hayley would need to perform approximately 86 haircuts in a month for the total amount paid to either salon to be the same.

Now, to calculate the total amount paid to either salon, we can use the following formulas:

Total amount paid at The Princeton Salon = Monthly rent + Earnings (which would be all of her earnings, as mentioned in the prompt)

Total amount paid at the franchise = Cost per haircut * Number of haircuts

Plugging in the values:

Total amount paid at The Princeton Salon = $774 + (Earnings from haircuts)

Total amount paid at the franchise = $9 * 86

Since the total amount paid to either salon is the same, we can equate the two equations:

$774 + Earnings from haircuts = $9 * 86

Solving for Earnings from haircuts:

Earnings from haircuts = $9 * 86 - $774

Earnings from haircuts = $774

So, Hayley would pay a total of $774 in earnings from haircuts, regardless of whether she chooses self-employment at The Princeton Salon or working at the franchise. The number of haircuts she needs to perform to reach this amount is 86.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE

According to the question the magnitude of the resulting force is 5.83.

Magnitude is a measure of the size or intensity of a physical quantity. It is an expression of how large or small a quantity is in comparison to a reference value. Magnitude is typically used in physics and astronomy, but it can also be used in other areas such as engineering and seismology. Magnitude is not an absolute measurement; rather, it is a relative measure of how much larger or smaller one quantity is compared to another. For example, the magnitude of a star's brightness is a measure of how much brighter it is compared to other stars.

The magnitude of the resulting force can be calculated using the Pythagorean theorem. The formula for calculating the magnitude of a vector is:
[tex]\sqrt[]{(x2 + y2)}[/tex]
In this case, x = 5 and y = -3, which gives us:
[tex]\sqrt{(52 + (-3)2)}[/tex] = [tex]\sqrt{(25 + 9)}[/tex] = √[tex]\sqrt{(34)}[/tex] = 5.83.
Therefore, the magnitude of the resulting force is 5.83.

To learn more about magnitude
https://brainly.com/question/28047791
#SPJ1

Answer:

Looking at the number line, we can see that R is to the left of P, and S is to the right of P. Also, Q is to the left of R, and S is to the right of Q.

So, the first statement "R x P > S" is not true, because S is to the right of both R and P.

The second statement "S > Q x R" is also not true, because Q is to the left of R, and S is to the right of both Q and R.

The third statement "Q x R > S" is true, because Q is to the left of R, and S is to the right of both Q and R. Therefore, the correct statement is:

Q x R > S