A candy store sells a brand of nuts that costs $2 per pound and a brand of chocolate coated candies that costs $0.95 per pound. Select the equation that solves for x lb of nuts that must be mixed with 32 lb of the chocolate coated candies in order to have a mixture that costs 1.48 per pound.

A. 2x + 0.95(32) = 1.48x
B. 2x + 0.95(32) = 1.48(x + 32)
C. 0.95x + 2(32) = 1.48(x + 32)
D. 0.95x + 2(32) = 1.48x
E. none of these

Answer:

4/23

Step-by-step explanation:

I Did The Quiz :)

Answer:

M (-4; 4)

Step-by-step explanation:

A ( -6; 1), B ( -2; 7)

M (midpoint) = ( ?; ?)

Midpoint coordinates formulas are

x = (x1 + x2) / 2

y = (y1 + y2) / 2

xM = (xA + xB) / 2 =

= (-6 + (-2)) / 2 = (-6 - 2) / 2 = -8 / 2 = -4

yM = (yA + yB) / 2 =

= (1 + 7) / 2 = 8 / 2 = 4

M (-4; 4)

The measures of angles of a rhombus are ∠KNL = 90° , ∠KJL = 50° , ∠MLK = 100° and ∠JKM = 40°

A Rhombus has four sides of the same length, its perimeter can be determined using the formula Perimeter = 4a, where "a" stands for the side's length.

When the two diagonals of a rhombus are known,

The perimeter = 2√p² + q²

where 'p' and 'q' are the diagonals.

Given data ,

Let the rhombus be represented as JKLM

where MK and JL are the diagonals and N is the midpoint of intersection

The measure of MK = 24

The measure of JL = 20

The measure of NK = 12

The measure of ∠MJL = 50°

Now , the diagonals of a rhombus bisect each other , so

NK = MK/2 = 12

And , NL = JL / 2 = 10

Now , to calculate the measure of ML ,

In triangle MNL, ∠N = 90°

MN = NK = 12 , NL = 10

Using Pythagorean theorem of triangles , we get

ML² = MN² + NL²

ML² = 12² + 10²

ML² = 244

ML = √244

On simplifying the equation , we get

ML = 2√61 = 15.62

The measure of ML = measure of JM = 15.62 ( all sides are equal )

The measure of ∠KNL = 90° ( diagonals of a rhombus are perpendicular bisectors )

∠KJL = ∠MJL (diagonals bisect angles)

The measure of ∠KJL = 50°

∠MJK = ∠KJL + ∠MJL = 50 + 50 = 100°

∠MJK = ∠MLK (opposite angles are equal)

The measure of ∠MLK = 100°

∠NJK + ∠JNK + ∠JKM = 180° (sum of angles in triangle)

50 + 90 + ∠JKM = 180

The measure of ∠JKM = 40°

∠JKL = 2 x ∠JKM (diagonal bisect angle)

The measure of ∠JKL = 2 x 40

The measure of ∠JKL = 80°

∠JKL = ∠JML (opposite angles are equal)

The measure of ∠JML = 80°

Hence , the measures of rhombus is solved

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Answer:

D

Step-by-step explanation:

[tex]100(1 + \frac{016}{12}) ^{12(20)}[/tex]

331.02

Answer:

D. $220.00

Explanation :

Pt(1+r/n) n

Answer:

(x + 7)(x - 3) = 75 square feet.

Step-by-step explanation:

Given that x represents the side length of the mural in Ashwin's classroom, the hallway mural's length is x + 7 feet and its width is x - 3 feet. The area of the hallway mural can be found by multiplying these two binomials, (x + 7)(x - 3), to get x^2 + 4x - 21.

If each side of the classroom mural is 8 feet long, the hallway mural would have sides of 15 feet and 5 feet, so its area would be 75 square feet, which is the answer.

The equation for the perimeter will be (4/5)d + 18d = 282. The value of d is 15.

The perimeter of any two-dimensional figure is defined as the sum of all the sides of the figure. For a trapezoid, the perimeter will be the sum of all the sides of the trapezoid.

Given that the four sides of the figure are,

12d + 4

4/5d -9

2d

4d - 6

The perimeter of the figure is 271. The equation can be written as:-

(4/5)d - 9 +12d + 4 + 4d - 6 + 2d = 271

(4/5)d + 12 d + 4d + 2d -15 + 4 = 271

(4/5)d + 18d = 282

94d = 282 x 5

d = 15

Therefore, the perimeter will be calculated as (4/5)d + (18d) = 282. D has a value of 15.

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The three consecutive odd integers are 47, 49, and 51. The third number is 51, so the answer is (d) 51.


Let's represent the first odd integer as x. Then, the next two consecutive odd integers would be x + 2 and x + 4.

According to the problem, the sum of these three consecutive odd integers is 147:

x + (x + 2) + (x + 4) = 147

We simplify and solve for x, which gives us the value of the first integer.

Simplifying and solving for x, we get:

3x + 6 = 147

3x = 141

x = 47

So the three consecutive odd integers are 47, 49, and 51. The third number is 51, so the answer is (d) 51.

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To make 50 ounces of a 40 percentage alcohol solution, eight ounces of the 30% solution must be mixed with the 70% solution.

1. Round the two solutions' initial concentrations to the nearest tenth (30% alcohol = 0.3; 70% alcohol = 0.7).

2. Determine the combined solution's overall alcohol content

(30% + 70%): 0.3 + 0.7 = 1.

3. Multiply 50 ounces by 0.4 to get the total amount of alcohol required for a 40% solution:

50 x 0.4 = 20 ounces.

4. Determine how much 30% solution is required to reach the desired concentration. 1 divided by 20 equals 20 ounces.

5. Subtract the quantity of the existing 70% solution:

(50 ounces x 0.7)/20 ounces = 8 ounces.

6. The outcome is that 8 ounces of the 30% solution are required to create 50 ounces of the 40% solution.

The original concentrations of the two solutions must first be converted to decimals (30% alcohol = 0.3; 70% alcohol = 0.7) in order to determine how much of a 30% alcohol solution has to be added to a 70% alcohol solution to create 50 ounces of a 40% alcohol solution. The two decimals can then be added to determine the total amount of alcohol present in the combined solution: 0.3 + 0.7 = 1. In order to determine the entire amount of alcohol required for a 40% solution, multiply 50 ounces by 0.4, which results in 20 ounces. The amount of the 30% solution required to reach the specified concentration can be estimated by dividing 20 ounces by 1, which is 20 ounces. Then, 20 ounces must be divided by the amount of the 70% solution that is already present to get 8 ounces. As a result, 8 ounces of the 30% solution are required to create 50 ounces of the 40% solution.

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a)  The test was designed to have a 5% chance of making a Type I error. b) Reject H0 since p-value < significance level. c) Type I error (false positive) if H0 is true and rejected.

A significance test is used to determine whether there is sufficient evidence to reject a null hypothesis, which is a statement about a population parameter, such as a proportion, mean, or standard deviation. The significance level, often denoted by α, is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. The commonly used significance level is 0.05, which means that the test is designed to have a 5% chance of making a Type I error.

In this scenario, the sample proportion is 0.12 and the p-value is 0.03, which is the probability of observing a sample proportion as extreme as 0.12 or more extreme, assuming that the null hypothesis is true. Since the p-value is less than the significance level, we have strong evidence against the null hypothesis, and we reject it. Therefore, we conclude that the proportion is significantly different from the hypothesized value.

If the null hypothesis is actually true, and we reject it based on the sample data, we have made a Type I error. In other words, we have falsely concluded that there is a difference when there is not. False positive is another name for this mistake. Conversely, a Type II error occurs when we fail to reject the null hypothesis when it is actually false, and this error is also known as a false negative.

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The complete question is:

A significance level of 0.05 is used when conducting a proportion-related significance test. 0.12 is the sample statistic. P-value equals 0.03.

a) What chance of a Type I error was the test designed for, if H0 were true?

b) What judgement would you draw on this test (reject or fail to reject)?

c) What kind of error, if any, was there as a result of this test?

Answer:

Step-by-step explanation:

The total volume of lemonade held by 24 bottles would be 18,000 mL (750 mL x 24) or 24x 0.75 liters = 18 liters.

And it would be to express the total volume in terms of the volume of one bottle. You can say that 24 bottles of lemonade is equal to 18 times the volume of one bottle, or 18 x 750 mL = 18,000 mL. This can also be written as 24 x 0.75 liters = 18 liters. This can also be expressed as 18 liters, since 1 liter is equal to 1000 mL.

Regardless of how you choose to express the answer, both methods give us the same result: 24 bottles of lemonade hold a total of 18,000 mL or 18 liters of the beverage. This information can be useful in various contexts, such as for planning a party or for ordering supplies for a lemonade stand. It's important to note that while both answers give the same result, they present the information in different ways. The first answer provides the total volume of lemonade held by all 24 bottles, while the second answer provides the number of times the volume of one bottle is contained within the total volume. Both answers provide useful information and the choice of which one to use may depend on the specific context in which the question is being asked.

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Answer: 54 is 18.24% of 296

Step-by-step explanation:

54:296*100 =

(54*100):296 =

5400:296 = 18.24

Now we have: 54 is what percent of 296 = 18.24

Question: 54 is what percent of 296?

Percentage solution with steps:

Step 1: We make the assumption that 296 is 100% since it is our output value.

Step 2: We next represent the value we seek with x

Step 3: From step 1, it follows that 100% = 296

Step 4: In the same vein, x% = 54

Step 5: This gives us a pair of simple equations:

100% = 296 (1)

x% = 54 (2)

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS (left-hand side) of both equations have the same unit (%); we have

100% over x% = 296 over 54

Step 7: Taking the inverse (or reciprocal) of both sides yields

x% over 100% = 54 over 196

x=18.54

The Cupcake Café’s recipe for cheesecake calls for 2/3 cup of cream cheese.42 cups of cream cheese does the café use to make 63 cheesecakes.

What is word problem?

A word problem is a mathematical problem or puzzle that is presented in the form of a written description or narrative, rather than as a simple equation or formula. It typically involves a scenario or situation that requires mathematical calculations or problem-solving skills to arrive at a solution. Word problems can be found in a variety of settings, including in math textbooks, standardized tests, and real-life situations. They often require the reader to identify and interpret relevant information, apply mathematical concepts and formulas, and use critical thinking skills to arrive at a correct answer.

To make 63 cheesecakes, the Cupcake Café would use:

(2/3 cup of cream cheese per cheesecake) x (63 cheesecakes)

= 42 cups of cream cheese.

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Answer:

x=7/6

Step-by-step explanation:

add 2/3 to both sides

Answer:

Step-by-step explanation: (a) To expand (1 + e^x) + (e^3x) in ascending powers of x to the term x^2, we can use the Taylor series expansion.

The Taylor series expansion for e^x is given by:

e^x = 1 + x + x^2/2! + x^3/3! + ...

So,

e^x = 1 + x + x^2/2! + x^3/3! + ...

and

e^3x = 1 + 3x + 9x^2/2! + 27x^3/3! + ...

Now, we can substitute these expansions into the original equation to get:

(1 + e^x) + (e^3x) = 1 + (1 + x + x^2/2! + x^3/3! + ...) + (1 + 3x + 9x^2/2! + 27x^3/3! + ...)

Expanding, we get:

(1 + e^x) + (e^3x) = 2 + x + 4x + x^2/2! + 9x^2/2! + ...

So, to the term x^2, the expansion becomes:

(1 + e^x) + (e^3x) = 2 + x + 4x + (x^2/2! + 9x^2/2!) + ...

which simplifies to:

(1 + e^x) + (e^3x) = 2 + x + 4x + 11x^2/2! + ...

(b) The coefficient of x^2 in the expansion is 11/2!. So, n = 11/2! = 11/2.

The answers include the following below:

This is referred to as the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Parallel lines refers to the type of lines that never cross one another and are the same distance apart at all times.

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If G is the midpoint of EH, FG= GI, then triangle EFG= triangle HIG

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Given G is the midpoint of EH,

FG≅ GI,

We need to Prove triangle EFG= triangle HIG

∠E and ∠H are right angles, FG≅ GI from given.

∠E≅  ∠H from given

G is midpoint of EH from given

EG≅ GH by definition of congruent triangles.

triangle EFG≅ triangle HIG by SAS congruence postulate.

Hence, if  G is the midpoint of EH, FG= GI, then triangle EFG= triangle HIG

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The third side is between 7 and 17 inches long.

This theorem states that for any triangle, the sum of the lengths of the first two sides will always be greater than the length of the third side.

A triangle's two sides have lengths of 5 and 12 inches.

According to the triangle Inequality (theorem), any triangle's two sides must add up to more than its third side.

The length of the third side will be,

5 + 12 = 17 inches

It is to be noted that the difference between the two sides cannot be less on the third side.

The third side must be greater than,

12 – 5 = 7 inches.

As a result, the third side's length ranges from 7 to 17 inches.

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The ratio of the sides' lengths of a triangle with sides of 30-60-90 is:

short leg : long leg : hypotenuse = 1 : √3 : 2

Consequently, the triangle's short leg's measurement is 8.

A triangle is a 3-sided shape with 3 vertices. The angles of the triangle are formed by the connection of the 3 sides end to end at a single point. The triangle's three angles sums up to 180 degrees.

Triangles can be divided into three varieties based on the lengths of their sides, which are:

Scalene.

Isosceles.

Equilateral.

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The answer is given below:

Binomial distribution is a discrete  probability distribution in which it gives two values that is either success or failure.

A local donut shop began putting an extra donut in some of the boxes.

The shop owner claimed that one in seven boxes had an extra donut.

Nine customers each bought one box of donuts at the shop.

Probability of success fixed is, [tex]p=\frac{1}{7}[/tex]

A value of n fixed, n=9.

We can use binomial distribution to solve this problem,

The probability mass function for the Binomial distribution is given as:

Assume  X is a binomial distribution, [tex]B(n=9,p=\frac{1}{7}=1.143)[/tex].

[tex]P(X)=(nCx)(p)^{x} (1-p)^{n-x}[/tex]

The mean is given by:

[tex]E(X)=np=9*\frac{1}{7}=1.29\\[/tex]

The variance is given by,

[tex]Var(X)=np(1-p)=9*\frac{1}{7}(1-\frac{1}{7} )[/tex]=1.1094

From variance, the standard deviation is given by, [tex]std(X)=\sqrt{1.1094}[/tex]=1.05.

Two of the nine customers buy a box of donuts with an extra donut. Compute P(X ≥ 2) and use the result to justify your answer.

[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)][/tex]

And if we find the individual probabilities we got,

[tex]P(X=0)=(9C0)(0.143)^{0} (1-0.143)^{9-0}=0.249\\P(X=1)= (9C1)(0.143)^{1} (1-0.143)^{9-1}=0.374[/tex]

[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)]\\[/tex]

                      = 1-[0.249+0.374]

                       = 0.377

Hence, [tex]P(X\ge2)=[/tex] 0.377.

This case makes sense the claim since the probability is higher or equal than the expected with the claim.

Corrected question:

To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes had the extra donut and the shop owner claimed that one in seven boxes had an extra donut. Nine customers each bought one box of donuts at the shop. Let X = the number of customers that bought a box containing an extra donut.A. Is X a binomial random variable? Explain.B. What is the mean and standard deviation of X? Provide an interpretation for each value in context.C. Two of the nine customers buy a box of donuts with an extra donut. Is the shop's claim accurate? Compute P(X ≥ 2) and use the result to justify your answer.

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Answer:

Radius is 3 units

Center is (0,5)

Step-by-step explanation:

Compared to the standard form of the equation of a circle, [tex](x-h)^2+(y-k)^2=r^2[/tex], we have a center of [tex](h,k)\rightarrow(0,5)[/tex], and a radius of [tex]r=3[/tex].

The indirect speech version of the given sentence would be:

She said that her mother was cooking food.

Indirect speech (also known as reported speech) is a way of expressing what someone else said, without using their exact words. In indirect speech, we usually report the statement or question using a reporting verb like "say", "tell", "ask", or "explain", followed by a conjunction such as "that". We also need to change the tense and sometimes the pronouns to reflect the new context.

Indirect speech is often used in writing and speaking to convey someone else's message, opinion or idea. It helps us to paraphrase or summarize what someone else said, without quoting them directly. It is important to learn how to use indirect speech correctly, as it is a common feature of both formal and informal communication.

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The standard deviation of the number of lemons used is equal to 14.7.

Mathematically, the mean for these set of data would be calculated by using this formula:

Mean = [F(x)]/n

F(x) = 47 + 45 + 61 + 44 + 16

F(x) = 213.

Mean = 213/5

Mean = 42.6

Next, we would calculate the standard deviation of this data set by using this formula:

SD = √(1/n × ∑(xi - u₁)²)

SD = √(1/5 × (47 - 42.6)² + (45 - 42.6)² + (61 - 42.6)² + (44 - 42.6)² + (16 - 42.6)²)

Standard deviation, SD = √(1073.2/5)

Standard deviation, SD = 14.7.

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The frequency of each class interval 103 - 107, 108 - 112 and 113 - 117 are 2, 2 and 4 respectively.

A grouped frequency distribution is the distribution of data into various classes with equal width with the frequency being the number of outcomes in that class.

Given are the hottest recorded temperatures (in °F) for eight cities throughout North America.

113   110   108   104   117   116   113   103

The class intervals are 103 - 107, 108 - 112 and 113 - 117.

In the distribution, the frequency of a class is the number of temperatures that class.

The temperatures in the class 103 - 107 are 103 and 104.

Frequency of 103 - 107 = 2

The temperatures in the class 108 - 112 are 108 and 110.

Frequency of 108 - 112 = 2

The temperatures in the class 113 - 117 are 113, 113, 116 and 117.

Frequency of 113 - 117 = 4

Hence the frequency are 2, 2 and 4 for the intervals 103 - 107, 108 - 112 and 113 - 117 respectively.

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Answer:

160 pounds of algae

Step-by-step explanation:

10 times 2 is 20   ( first 5 hours )

20 times 2 is 40  (10 hours)

40 times 2 is 80 (15 hours)

80 times 2 is 160 ( 20 hours)

there would be 160 pounds of algae

4x³ + 9x² - x - 6 is a volume of the container.

What does volume mean in plain terms?

Any three-dimensional solid's volume is just the amount of space it takes up. These solids can have the shape of a cube, cuboid, cone, cylinder, or sphere.

                                The 3-dimensional space that is occupied by matter or surrounded by a surface is measured in volume, which is expressed in cubic units. A derived measure called the cubic meter (m3) serves as the SI unit of volume.

= (4x-3) . (x+1) . (x+2)

= [ 4x .x + 4x . 1 - 3x - 3] . ( x + 2)

= ( 4x² + 4x - 3x - 3 ) ( x + 2 )

= ( 4x² + x - 3 ) ( x+ 2 )

= 4x³ + x² - 3x + 8x² + 2x - 6

 = 4x³ + 9x² - x - 6

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Answer:

[tex]\huge\boxed{\sf -3x\² + x + 5}[/tex]

Step-by-step explanation:

g(x) = 4x + 5

f(x) = -3x² - 3x

= 4x + 5 + (-3x² - 3x)

= 4x + 5 - 3x² - 3x

= 4x - 3x + 5 - 3x²

= x + 5 - 3x²

[tex]\rule[225]{225}{2}[/tex]

The expected value of the policy for the insurance company: $359.38

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The expected value of the policy for the insurance company can be calculated as follows:

Expected value = (Probability of survival) x (Annual payment)

= 0.999057 x $360

= $359.38

So, the expected value of the policy for the insurance company is $359.38.

It's important to note that this is just an estimate based on statistical probabilities and does not guarantee the outcome. The actual value could be higher or lower than this estimate, depending on the actual lifespan of the policyholder.

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