Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each value to the correct expression.
22
0
5
8
27
1+5.2 + (1 + 3)² ←
4 + 8(+2)
0.25 4³1
15
Reset
Next

The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.

The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.

The point of intersection is (-6, 10).

We have,

To sketch the graph of the system of equations:

x + y = 4

2x + 3y = 18

We can start by solving each equation for y:

y = -x + 4

y = (-2/3)x + 6

Then, we can plot a few points on each graph by choosing values of x and solving for y.

Here are three points for each graph:

x + y = 4:

x = -4, y = 8: (-4, 8)

x = 0, y = 4: (0, 4)

x = 4, y = 0: (4, 0)

2x + 3y = 18:

x = 0, y = 6: (0, 6)

x = 3, y = 4: (3, 4)

x = 9, y = 0: (9, 0)

To plot the graphs, we can use these points and draw a straight line through each set of three points.

The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.

The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.

To find the point of intersection, we can solve the system of equations:

x + y = 4

2x + 3y = 18

One way to solve this system is to use substitution.

We can solve the first equation for x:

x = 4 - y

Then we can substitute this expression for x into the second equation and solve for y:

2(4 - y) + 3y = 18

8 - 2y + 3y = 18

y = 10

Now that we know that y = 10, we can substitute this value into either equation to solve for x:

x + y = 4

x + 10 = 4

x = -6

So the point of intersection is (-6, 10).

Thus,

The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.

The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.

The point of intersection is (-6, 10).

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The the freshness half-line of milk is 10h, (b) The milk keep fresh at 22°C  for 31.1h (c) The milk keep fresh at 4°C for 55.7h

Recal that Storage temperature refers to the temperature at which food product is stored immediately after preparation and maintained at a safe holding temperature until it is dispensed to the customer

The given relation is T = 190 (1/2)^t/10

a. From the relation, T = 190 (1/2)^t/10

So the freshness half life of milk is 10 hours

b.  22 =  190 (1/2)^t/10

t = 10log₁/₂(190/22) = 31.1 hours

c. = 190 (1/2)^t/10

t= 10log₁/₂(190/22 = 55.7 hours

Milk can keep fresh for 55.7 hours at 4°C

Learn more about storage temperature on https://brainly.com/question/26314720

#SPJ1

Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

To know more about density

https://brainly.com/question/29775886

#SPJ1

Answer:

We can use a Venn diagram to visualize the information given in the problem.

Let M, B, and C represent the sets of students who pass mathematics, biology, and chemistry, respectively. We are given the following information:

|M| = 10 (the number of students who pass mathematics)

|B| = 30 (the number of students who pass biology)

|C| = 25 (the number of students who pass chemistry)

|M ∩ B| = 11 (the number of students who pass both mathematics and biology)

|B ∩ C| = 10 (the number of students who pass both biology and chemistry)

|M ∩ C| = 7 (the number of students who pass both mathematics and chemistry)

|M ∩ B ∩ C| = ? (the number of students who pass all three subjects)

We know that:

| M ∪ B ∪ C | = |M| + |B| + |C| - |M ∩ B| - |B ∩ C| - |M ∩ C| + |M ∩ B ∩ C|

Substituting the given values:

| M ∪ B ∪ C | = 10 + 30 + 25 - 11 - 10 - 7 + |M ∩ B ∩ C|

Simplifying:

| M ∪ B ∪ C | = 37 + |M ∩ B ∩ C|

We also know that:

| M ∪ B ∪ C | = 70 (the total number of students)

Substituting the value:

70 = 37 + |M ∩ B ∩ C|

Simplifying:

|M ∩ B ∩ C| = 33

Therefore, 33 students pass all three subjects.

Step-by-step explanation:

pls mark branliest i beggggg u

Answer: [tex]0.4x=360,000[/tex]

Step-by-step explanation:

From the problem it can be seen that 360,000 is 40% of the sales she got this year. So, 40% of her sales is 360,000.

40% of x is mathematically 0.4 times x.

Therefore the equation you could use is:  [tex]0.4x=360,000[/tex]

If you want to solve this for x, simply divide 0.4 from both sides to get x by itself.

[tex]x=(\frac{360,000}{0.4})=900,000[/tex]

So this year she made 900,000 dollars.

The volume of the funnel to the nearest tenth of a unit is approximately 341.4 cubic inches.

What is volume?

Volume is a measure of the amount of space that a three-dimensional object occupies. It is the quantity of space that is enclosed within a closed surface, and is typically measured in cubic units, such as cubic meters ([tex]m^3[/tex]), cubic centimeters ([tex]cm^3[/tex]), cubic feet ([tex]ft^3[/tex]), or gallons (gal).

We can use the formula for the volume of a cone to find the volume of the funnel, since a funnel is essentially a cone with a hole at the top. The formula for the volume of a cone is:

[tex]V = (1/3)\pi r^2h[/tex]

where V is the volume, r is the radius of the circular base, and h is the height of the cone.

Since the funnel has a diameter of 9 inches, its radius is half of that, or 4.5 inches. The height of the funnel is given as 16 inches.

Plugging these values into the formula, we get:

[tex]V = (1/3)\pi(4.5 in)^2(16 in)\\\\= (1/3)\pi(20.25 in^2)(16 in)[/tex]

≈ [tex]341.4 in^3[/tex]

Rounding this answer to the nearest tenth of a unit, we get:

V ≈ [tex]341.4 in^3[/tex]

Therefore, the volume of the funnel to the nearest tenth of a unit is approximately 341.4 cubic inches.

To learn more about volume visit:

https://brainly.com/question/463363

#SPJ1

Answer:

3/2

Step-by-step explanation:

Answer:

  (c)  2/3

Step-by-step explanation:

You want the slope of the line through points (-3, -1) and (3, 3).

The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (3 -(-1))/(3 -(-3)) = 4/6 = 2/3

The slope of the line is two thirds, choice C.

<95141404393>

For the given problem, a.)The unicycle covers 1.885 meters, in one revolution of wheel. b.) The wheel must rotate 53 times to cover distance of 100 metres.

a.) The circumference of a unicycle's wheel is determined by

                               [tex]\qquad \qquad C = \pi d\\ \text {where, d is the diameter of the wheel. }[/tex]

As a result, the unicycle moves C metres when the wheel revolves once.

Now, on substituting d = 60 cm and π= 3.14.

We obtain,

[tex]C\approx 188.5 cm = 1.885 m[/tex]  (∵ 1m = 100cm)

As a result, when the wheel revolves once, the unicycle goes 1.885 metres.

b.) Now, Distance covered in one rotation by wheel =  [tex]C = 1.885 m[/tex]

To travel 100 metres, wheel need to rotate = 100/C times.

As a result, the number of full rotations necessary is:

[tex]100/C = 100/1.885 = 53.0504 \;rotations[/tex]

Thus, To traverse 100 metres, the wheel must rotate 53.04 times or 53 times( in nearest whole number )

Learn more about Circumference here:

https://brainly.com/question/28757341

#SPJ1

Answer:

  (b)  0.4

Step-by-step explanation:

You want the experimental probability that Antonia will make both of her next two free throw attempts.

The "experimental" probability is the fraction of times the outcome of interest occurred in the trials used for the experiment.

Here, Antonia made both free throws in trials 2, 5, 9, and 10 of the ten trials, so her record for making both free throws is 4 out of 10 trials. We are to assume this 4/10 ratio is the probability that the next 2 attempts will result in Antonia making both free throws.

The experimental probability of making both free throws is 0.4, choice B.

<95141404393>

The answer is 46 dollars

The inverse of the matrix A by getting its determinant value is equal to [tex]A^{-1} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]

The matrix is equal to,

A = [tex]\left[\begin{array}{ccc}4&2\\3&2\end{array}\right][/tex]

To find the inverse of a matrix,

we first need to calculate its determinant of the matrix A  we have,

|A| = [tex]\left|\begin{array}{ccc}4&2\\3&2\end{array}\right|[/tex]

⇒ |A| = 4(2) - 2(3)

        = 8 - 6

        = 2

Now we can proceed to find the inverse of A.

Set up the matrix of cofactors.

The matrix of cofactors C is obtained by replacing each element of A with its corresponding cofactor,

which is the determinant of the submatrix obtained by deleting the row and column that contain that element.

For our matrix A, we have,

C = [tex]\left[\begin{array}{ccc}2&-3\\-2&4\end{array}\right][/tex]

Transpose the matrix of cofactors.

The transpose of a matrix is obtained by flipping its rows and columns. For our matrix C, we have.

[tex]C^{T} = \left[\begin{array}{ccc}2&-2\\-3&4\end{array}\right][/tex]

Divide by the determinant.

The inverse of A is obtained by dividing the transpose of the matrix of cofactors by the determinant of A.

For our matrix A, we have,

A⁻¹ = [tex]C^{T}[/tex] / |A|

   [tex]C^{T} = (1/2)\left[\begin{array}{ccc}2&-2\\-3&4\end{array}\right][/tex]

   [tex]C^{T} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]

Therefore, the inverse of the matrix A is equal to [tex]A^{-1} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]

learn more about inverse of a matrix here

brainly.com/question/12537023

#SPJ1

The triangles ΔFGH and ΔLJK are similar triangles. Then the correct option is B.

Given that:

The diagram is shown.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The ratio of the corresponding sides of the triangle ΔFGH and ΔLJK is given as,

FG / JL = HF / LK = GH / JK

32/8 = 36/9 = 48/12

4 = 4 = 4

The ratio of the corresponding side will be equal. Then the triangles ΔFGH and ΔLJK are similar triangles. Then the correct option is B.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ1

Answer:

A. Quadratic

Step-by-step explanation:

The equation y=x^2+7x-15 is a quadratic equation. It might be the result of a quadratic regression.

_____

The descriptors "linear," "quadratic," "exponential," and "power" describe the sort of equation that is used to try to match the data. Quadratic regression returns a quadratic equation.

Answer:

radians = degrees x π/180

Therefore, to convert 300 degrees to radians, we have:

radians = 300 x π/180

radians = 5π/3

So, 300 degrees is equal to 5π/3 radians.

Answer: Your answer is 504 or if you want it differently it's 84x+252

Hope it helped :D

Answer:

Step-by-step explanation:

A randomized controlled trial is the best type of study to conduct to establish causality due to its ability to control for confounding factors, and its ability to measure the true effects of a particular treatment.

What is statistics?
Statistics is the science of collecting, organizing, analyzing, and interpreting data. It involves describing, summarizing, and making inferences about a given set of data. Statistics is used to make decisions in various fields, such as business, economics, medicine, psychology, and engineering. Statistical methods are used to help scientists understand the behavior of complex systems, to analyze the relationships between different variables, and to test hypotheses. Additionally, statistics can be used to draw conclusions from data, to identify patterns, to estimate probabilities, and to make predictions.

In order to establish causality, the best type of study to conduct is a randomized controlled trial (RCT). An RCT is a type of experiment designed to establish a cause-and-effect relationship between variables. This study involves randomly assigning individuals to different experimental groups, and then comparing the outcomes between the groups. This helps to determine the effects of a particular treatment or intervention on a population.

For example, if we wanted to study the effects of a new medication on a particular condition, we would create two groups of people – one group would receive the medication and the other would receive a placebo. We would then measure the outcomes of the two groups to see if the medication has an effect on the condition. This type of study helps to establish a causal relationship between the treatment and the outcome, as the randomization helps to control for other confounding factors that could influence the results.

Therefore, a randomized controlled trial is the best type of study to conduct to establish causality due to its ability to control for confounding factors, and its ability to measure the true effects of a particular treatment.

To know more about statistic click-
https://brainly.com/question/15525560
#SPJ1

(a) The test statistic is z = -1.788 and (b) P-value = 0.0734.

Hypothesis testing is a statistical method used to make decisions about a population based on a sample of data.

The process involves setting up a null hypothesis (H₀) and an alternative hypothesis (Hₐ), collecting data from a sample, calculating a test statistic based on the sample data, and using the test statistic to determine whether to reject or fail to reject the null hypothesis

Here we have

An article published in the Washington Post claims that 45 percent of all Americans have brown eyes.

A random sample of n = 78 college students found 30 who had brown eyes. Consider testing = H₀: p =0 .45 Hₐ:p + 0.45

(a) The test statistic can be calculated using the formula:

z = (p' - p) / √(p(1-p) / n)

where p' is the sample proportion, p is the hypothesized proportion under the null hypothesis, and n is the sample size.

In this case, the hypothesized proportion is p = 0.45, the sample proportion is p' = 30/78 = 0.3846 (rounded to four decimal places), and the sample size is n = 78. Therefore:

z = (0.3846 - 0.45) / √(0.45 × 0.55 / 78)

z = -1.788

So the test statistic is z = -1.788.

(b) To find the p-value, we need to look up the area in the standard normal distribution table corresponding to the test statistic z = -1.788. The area to the left of z = -1.788 is 0.0367 (rounded to four decimal places). Since this is a two-tailed test (Ha: p > 0.45), we need to double this area to get the p-value:

p-value = 2 × 0.0367

p-value = 0.0734 (rounded to four decimal places)

Therefore,

(a) The test statistic is z = -1.788 and (b) P-value = 0.0734.

Learn more about Hypothesis testing at

https://brainly.com/question/30588452

#SPJ1

Complete Question:

REMINDER: DO NOT use your calculator or an app to obtain normal curve areas such as you would for finding a p-value. Use the table in your formula packet. DO NOT use another method or the difference in precision may cause you to lose points. An article published in the Washington Post claims that 45 percent of all Americans have brown eyes. A random sample of n = 78 college students found 30 who had brown eyes. Consider testing = H₀: p= 0.45 Hₐ:p + 0.45 (a) The test statistic is z = -1.161 (b) P-value =

Based on the given table, the annual premium per $100 of coverage for a wood house in the country would be 0.74.

To calculate the annual premium for the $200,000 house, we first need to determine the coverage amount. Assuming a coverage of 80% of the house's value, the coverage amount would be:

Coverage amount = 80% of $200,000 = $160,000

Next, we can calculate the annual premium as follows:

Annual premium = (Coverage amount / $100) x Annual premium per $100 of coverage

= ($160,000 / $100) x 0.74

= $1,184

Therefore, the annual premium to insure the $200,000 wood house in the country would be $1,184.

The percentage with a 95% confidence interval that has an error bound of at most 3%.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". For example, if there are 20 red marbles out of 100 marbles in a jar, we can say that the percentage of red marbles is 20%. Similarly, if a store offers a 10% discount on a $50 item, the discounted price would be $45.

Percentages are commonly used to represent proportions or rates in various contexts, such as finance, and science. They allow us to easily compare and communicate numbers on a standardized scale, making it easier to interpret and analyze data.

To estimate the required sample size, we need to use the following formula:

n = (z*σ / E)^2

where:

n is the sample size we need to estimate the percentage with the desired error bound

z is the z-score for the desired level of confidence (95% in this case), which is 1.96

σ is the standard deviation of the population (unknown)

E is the desired margin of error, which is 3% of the percentage we are trying to estimate

Since we do not know the standard deviation of the population, we can use a conservative estimate of 0.5 (which gives the largest possible sample size).

Substituting the values we have:

n = (1.96 * 0.5 / 0.03)^2

n = 1067.11

So we would need to poll at least 1068 students to estimate the percentage with a 95% confidence interval that has an error bound of at most 3%.

To learn more about percentage click:

https://brainly.com/question/24877689

#SPJ1

Answer:

Step-by-step explanation:Answer 1 person found it helpful Davis Holmes These outcomes are only estimates of the real odds because they relied on Samara's 100 trials. The measured rates should approach the actual odds as she keeps rolling the dice.Which four kinds of probability are there?Mathematics' study of chance events is known as probability, and there are four major kinds of probability: axiomatic, classical, observational, and subjective.After three tries, Samira is expected to receive a 6.There is approximately a 9% chance that Samira will roll the dice more than 4 times to get a 6.Frequency:1: 162: 143: 134: 9more than 4: 48Note: These results are based on Samira's 100 trials, so they are only an estimate of the actual probabilities. As she continues to roll the dice more times, the observed frequencies should approach the true probabilities.To know more about Probability

Answer:  (11) Julius asks Rachel if she would like to sell her boat. Rachel privately has no interest in selling her boat and believes that Julius can't afford her boat anyway. Rachel says, "I'd sell my boat to you for $20,000." To Rachel's surprise, Julius responds "Ok, it's a deal." Rachel does not want to sell the boat to Julius for any price. Julius and Rachel have:

Answer:

[tex] \sf \: c \: = \: 28.3[/tex]

Step-by-step explanation:

To find the circumference of a circle .

We have to use the formula,

Where, C = [tex] 2 \pi r [/tex]

[tex] \pi [/tex] = 3.142

[tex] r [/tex] = 4.5m

So,

C = 2 × 3.142 × 4.5

C = 28.278 ≈ 28.3

Answer: 28.3

Step-by-step explanation:

C=2[tex]\pi r[/tex]

=2[tex]\pi[/tex](4.5)

=28.3 m

Answer: 92 ft²

Step-by-step explanation:

To find the surface area of a right prism, we will find the area of each side and add them together. We have three sets of two congruent sides. We will write an equation representing the area of these sides, set it equal to the surface area, and solve by simplifying.

2(8 ft * 3 ft) + 2(3 ft * 2 ft) + 2(8 ft * 2 ft) = Surface Area

2(24 ft²) + 2(6 ft²) + 2(16 ft²) = Surface Area

48 ft² + 12 ft² + 32 ft² = Surface Area

92 ft² = Surface Area

Answer: You might want to know how many 24 apples are, individually, also being an accountant, mathematician, scientist, all require Math and math follows PEMDAS [Parenthesis, exponents, multiplication, division, addition, subtraction.] normally.

Step-by-step explanation:

Also, if you multiple something let's say 378x54 and get 20,412 and let's say you want to divide this huge number to a smaller number you can divide from 2 all the way up! Mathematics is not just something we have to learn, it's also something we can use!

Answer:

Median: As this is a set of 8, add the two numbers which are in the middle (11 and 13) and then divide them by two.

Mean: Add all of the numbers in the set and then divide the answer by the total number of the numbers in the set, which is 8.

Step-by-step explanation:

cutive Function Test aimed at elderly individuals be a useful tool?

Using the standard thumb, we can say that any brain volume that falls outside the range of 878.6 cm³ to 1333.8 cm³ is significantly low or significantly high. Therefore, any brain volume below 878.6 cm³ or above 1333.8 cm³ would be considered significantly low or significantly high.

As for whether a Brain Executive Function Test aimed at elderly individuals would be a useful tool, the information given is not enough to answer that question. The Brain Executive Function Test is a cognitive assessment tool that measures various cognitive skills such as attention, problem-solving, working memory, and decision-making. The usefulness of this test depends on the purpose of the assessment and the population being tested. The given information only provides brain volume data of 20 brains and does not give any indication of the age or cognitive status of the individuals. Therefore, it is not possible to determine whether a Brain Executive Function Test aimed at elderly individuals would be useful based on this information alone.

The missing angle C of the given triangle using law of cosine is: 62.1°

The Law of Cosines is defined as a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.

Numerically, the Law of Cosines can be communicated as:

c² = a² + b² - 2abcos(C),

where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.

Thus:

90² = 55² + 50² - 2(55 * 50)cos(C),

2575 = 5500 cos C

2575/5500 = cos C

cos C = 0.4682

C = cos⁻¹0.4682

C = 62.1°

Read more about law of cosine at: brainly.com/question/4372174

#SPJ1

A reasonable prediction for the number of times the event of landing on an even number will occur in 550 rolls is 275.

When rolling a fair 6-sided die, there are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5). Therefore, the probability of rolling an even number is 3/6 or 1/2.

To predict the number of times the event of landing on an even number will occur in 550 rolls, we can multiply the probability of rolling an even number by the total number of rolls:

Expected number of even rolls = Probability of rolling an even number x Total number of rolls

Expected number of even rolls = (1/2) x 550

Expected number of even rolls = 275

Therefore, a reasonable prediction for the number of times the event of landing on an even number will occur in 550 rolls is 275.

To learn more about probability here

https://brainly.com/question/30034780

#SPJ1