Can you please help me with the problems shown, and please show the work

Answer:

80.

Step-by-step explanation:

When multiplying if the tenth place is " 7" then we look " next door" which is the ones and 8 is great then 5 so we count to from 8 to see when the next number ending in 0 would be in this case its 80. ( if the number is 4 or less count backwards to a number ending with 0  which in that case would have been 70 ) but the answer is 80.

Answer:

y=2x-2

Slope = 4.000/2.000 = 2.000

x-intercept = 2/2 = 1

y-intercept = -2/1 = -2.00000

y=3x-7

Slope = 6.000/2.000 = 3.000

x-intercept = 7/3 = 2.33333

y-intercept = -7/1 = -7.00000

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Answer:

(x,y)=(5,8)

y=8

x=5

Step-by-step explanation:

Method 1 ; Substitution Method

\(\begin{bmatrix}y=2x-2\\ y=3x-7\end{bmatrix}\\\\\mathrm{Subsititute\:}y=3x-7\\\\\begin{bmatrix}3x-7=2x-2\end{bmatrix}\\\\Isolate\:x \:for\:3x -7=2x-2\:\:,x=5\\\\\mathrm{For\:}y=3x-7\\\\\mathrm{Subsititute\:}x=5\\\\y=3\times\:5-7\\\\Simplify\\\\y=8\\\\y=8,\:x=5\)

Method 2 : Elimination Method

\(\begin{bmatrix}y=2x-2\\ y=3x-7\end{bmatrix}\\\\\mathrm{Arrange\:equation\:variables\:for\:elimination}\\\\\begin{bmatrix}y-2x=-2\\ y-3x=-7\end{bmatrix}\\\\y-3x=-7\\-\\\underline{y-2x=-2}\\-x=-5\\\\\begin{bmatrix}y-2x=-2\\ -x=-5\end{bmatrix}\\\\Solve\:-x=-5\:for\:x \:,x =5\\\\\mathrm{For\:}y-2x=-2\mathrm{\:plug\:in\:}x=5\\\\Solve \:y-2\times 5 =-2\:for\:y\:\: ,y =8\\\\y=8,\:x=5\)

Method 3 : Gaussian's Elimination

\(\begin{bmatrix}y=2x-2\\ y=3x-7\end{bmatrix}\\\\\mathrm{Arrange\:equation\:variables\:for\:elimination}\\\\\begin{bmatrix}y-2x=-2\\ y-3x=-7\end{bmatrix}\\\\\mathrm{Write\:a\:matrix\:with\:the\:coefficients\:and\:solutions}\\\\\begin{bmatrix}1&-2&¦&-2\\ 1&-3&¦&-7\end{bmatrix}\\\\Reduce \:matrix\:to\:echelon\:form\\\\\begin{bmatrix}1&0&¦&8\\ 0&1&¦&5\end{bmatrix}\\\\y=8,\:x=5\)

Answer:

3.398

Step-by-step explanation:

log(10) 2500 = log(10) (5^2*10^2) = log(10) 5^2 + log(10) 10^2 = 2*log(10) 5 + 2=3.398

Answer:

\(-1 \le x\le1.5\)

Step-by-step explanation:

The expression we're given, we want both to be defined because how can you add a defined number to an undefined number?

Square roots only have real solutions for positive numbers and zero

So let's set up an inequality for both square roots

\(2x+2\ge0\\\\6-4x\ge0\)

Let's solve the first one

\(2x+2\ge 0\\2x\ge-2\\x\ge-1\)

this is the domain of the "first expression"

let's solve the second one

\(6-4x\ge 0\\-4x\ge -6\\x\le 1.5\)

We want them to overlap, so we get a compound inequality: \(-1 \le x\le1.5\)

since we want both of the expressions to be defined to define the entire thing.

Answer

1. Solve for "y=" if necessary.

2. Substitute the value for "y" in the other equation.

3. Solve the new equation to find "x".

4. Substitute the value for "x" in either original equation to find "y".

5. Check your work.​

Explanation

1. Solve for "y=" if necessary.

2. Substitute the value for "y" in the other equation.

3. Solve the new equation to find "x".

4. Substitute the value for "x" in either original equation to find "y".

5. Check your work.​

Hope this Helps!!!

Answer:  \(C=31.4\)

Step-by-step explanation: When you are finding the circumference of a circle you use the formula

\(C=2\pi r\)

\(C=2*3.14 *5\)

\(C=31.4\)

Answer:

The second deal, 30 egg carton for $5, is better.

Step-by-step explanation:

1. Find how many eggs are in 3 dozen:

Dozen = 12    12 x 3 = 36

2. Find the value of 1 egg for each deal:

Deal 1: 36 eggs = $9

Divide 9 by 36, to find how much is 1 egg is:

9/36 = 0.25

Hence, in the first deal the value of 1 egg is 0.25 cents.

Deal 2: 30 eggs = $5

Divide 5 by 30, to find how much is 1 egg is:

5/30 = 0.16666666666 or 0.17

Hence, in the second deal the value of 1 egg is 0.17 cents.

3. Now we compare the two egg values:

Deal 1 value: 0.25 per egg

Deal 2 value: 0.17 per egg

If we look at the two values, the value for the second deals egg is cheaper than the value of the first deals egg, making the second deal better.

Answer:

Step-by-step explanation:

Discussion

Note: I think the length is supposed to be the height of 1 cookie.

The volume of the 12 cookies (1 dozen=12) is 176,715 in^3

The area of 1 cookie is 5 in

Area = pi * r^2

Area  of one cookie = 3.14 * 5^2

Area of one cookie = 78.5 in ^2 Note this is also the area of the base of the container.

Height of the 12 cookies = Volume / Area of one cookie

Height of the 12 cookies = 176.715/78,5

Height of the 12 cookies = 2.25 inches.

Answer

Thickness (height) of one cookie = 2.25/12

Thickness (height) of one cookie = .188 inches.

Answer:

45

Step-by-step explanation:

Replace everything in the equation that has a x to -3:

f(-3)=3(-3)^2-4(-3)+6

Square the -3:

f(-3)=3(9)-4(-3)+6

Multiply/Distribute

f(-3)=27+12+6

Add:

f(-3)=45

Hope this helps!

Answer:

f(x) = 45

Step-by-step explanation:

f (x) = 3x^2 − 4x + 6 find f (−3)

Replace the variable x with −3 in the expression.

f (−3) = 3(−3)^2 − 4 ⋅ −3 + 6

Simplify 3(−3)^2 − 4 ⋅ −3 + 6

Remove parentheses.

3(−3)^2 − 4 ⋅ −3 + 6

Raise −3 to the power of 2.

3 ⋅ 9 − 4 ⋅ −3 + 6

Multiply 3 by 9.

27 − 4 ⋅ −3 + 6

Multiply −4 by −3.

27 + 12 + 6

Simplify by adding numbers.

Add 27 and 12.

39 + 6

Add 39 and 6.

45

x = {x | x ≠ 0, x ≠ ±7} is the domain of the given function h(x)  = 9x/x(x²-49). So, Option B is the correct option.

Functions are used to assign outputs to inputs. A function's domain is the collection of all potential inputs to the function. The domain of f(x)=x2 is all real numbers, for example, whereas the domain of g(x)=1/x is all real numbers except x=0.

Consider the function y = f(x) to have an independent variable x and a dependent variable y. If a function f provides a technique to successfully create a single value y using a value for x, that chosen x-value is said to belong to f's domain.

The given function is  h(x)  = 9x/x(x²-49)

We need to determine the domain of this function.

Let us equate the denominator of the function to zero to find x value.

x(x²-49) = 0

x = 0

x²-49 = 0

x = ± 7

Thus, x = 0,-7,+7

So, domain can be intervals between the x values obtained but cannot be equal to the x values.

Therefore, x = {x | x ≠ 0, x ≠ ±7} is the domain of the given function h(x)  = 9x/x(x²-49). So, Option B is the correct option.

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Answer:

3000

Step-by-step explanation:

Tony will donates $3000 after 5 years.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Donated amount= $1000

Tony is able to donate 3/2 times the amount that Theresa donates.

let Theresa donates x dollar each year

So, x+ 3/2x = 1000

5x/2 = 1000

5x = 2000

x= 400

Thus, Tony donate = 3/2 x 400 = $600

Hence, After 5 years Tony will donate= 600 x 5= $3000

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Answer: First number = 3.5  , Second number = - 10.5

Step-by-step explanation:

Let two numbers be a and b

According to the question -

Sum = - 7      ...... ( 1 )

Difference = 14 ...... ( 2 )

so  :-         a + b = - 7  and a - b = 14

Now add both equations

( a + b ) + ( a - b ) = - 7 + 14

2a = 7

a = 7 / 2

a = 3.5

Now put value of a in equation ( 1 ) .........

a + b = - 7

3.5 + b = - 7

b = - 7 - 3.5

b = - 10.5

so first number = 3.5

second number = - 10.5

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Answer:

4.25

Step-by-step explanation:

she has a total of 20 dollars and she wats to buy ice cream each at 3.15 for a total of 5 people including her self.

so 3.15(5) is 15.75

then subtract 15.75 from 20

20 - 15.75 = 4.25

The distance between the intersection and the bank is equal to 77.0 feet.

In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

Note: Let the distance between the intersection and the bank be represented by the variable x.

By applying the properties of similar triangles, we have the following ratio of corresponding side lengths;

x/50 = 382/248

248x = 382(50)

x = 19,100/248

x = 77.0 feet.

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Complete Question:

The intersection of the two roads shown forms two similar triangles. If AC is 382 feet, MP is 248 feet, and the gas station is 50 feet from the intersection, how far from the intersection is the bank?

Answer:

The coordinates of the image B' is;

Explanation:

Given the figure in the attached image.

The coordinate of the Preimage B is;

Then rotating it 90 degrees in the counter-clockwise direction;

Applying the transformation to the given coordinate, we have;

Therefore, the coordinates of the image B' is;

Answer:

3x = 3 + 2y -------------> 3x - 2y = 3 {subtracted 2y from each side of top equation}

(-4/3)x + y = -2/3 ------> -4x + 3y = -2 {multiplied bottom equation by 3}

3x - 2y = 3 ------> 12x - 8y = 12 {multiplied top equation by 4}

-4x + 3y = -2-----> -12x + 9y = -6 {multiplied bottom equation by 3}

12x - 8y = 12

-12x + 9y = -6

--------------

y = 6 {added the two equations}

3x = 3 + 2y {original top equation}

3x = 3 + 2(6) {substituted 6, in for y, into top equation}

3x = 3 + 12 {multiplied}

3x = 15 {added}

x = 5 {divided each side by 3}

x = 5 and y = 6

Step-by-step explanation:

Answer:

x= 0

y= -1

Step-by-step explanation:

Hope this helps.

Answer: D (4,1)

Step-by-step explanation:

2x + 3(x-3) = 11

2x + 3x - 9 = 11

5x = 11 + 9

x = 20/5 = 4

y = x-3

= 4-3 = 1

Since 56 pints of Cold Farm ice cream cost $140, and 28 quarts of Cold Farm, ice cream cost $133, hence the large size container is the better deal for Sheldon.

From the table, we are told that 1 pint of Cold farm costs $2.50, this can be written as:

56pints of the cold farm will cost (56 * 2.50) = $140

Similarly, 1 quartz of Cold farm costs $4.75, this can be written as:

28pints of the cold farm will cost (28 * 4.75) = $133

56 pints of Cold Farm ice cream cost $140, and 28 quarts of Cold Farm, ice cream cost $133, hence the large size container is the better deal for Sheldon.

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Answer:

b<25

Step-by-step explanation:

Answer:

b ≥ 25.

Step-by-step explanation:

The statement contains the phrase “A minimum of” meaning that the amount of candy bard in each bag could either be anything higher than 25, or just 25. Basically just any number that is greater than or equal to 25. Therefore, you should use the greater than or equal to sign after the variable b and then but the number 25 after that.

I hope this helps you. Have a nice day.

For a hypothesis testing by considering two samples related to rate of people who exercise and who do not exercise, the observed t-value < standard so, null hypothesis does not rejected and there is no evidence to support the claim.

We have a researcher who was interested in making a comparison of resting pulse rate of people who exercise regularly and who do not exercise regularly. There is two independent samples. In 1ˢᵗ sample, sample size, n₁= 16

Sample mean, \(\bar X_1\) = 72.3

Standard deviations, s₁ = 10.3

In case of second sample, sample size, n₂ = 12

Sample mean, \( \bar X_2\) = 69.0

Standard deviations, s₂ = 8.9

Level of significance = 2.5% = 0.25

Consider the null and alternative hypothesis for the test hypothesis are defined as \(H_0 : μ_1 =μ_2\)

\(H_a : μ_1 >μ_2\)

The test statistic : using t-test formula

\(t = \frac{ \bar X_1 - \bar X_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}}}\)

\(= \frac{72.3- 69}{ \sqrt{ \frac {10.3^2}{16} + \frac{8.9^2}{12}}}\)

= 0.91

Degree of freedom, df = n1 + n2 - 2

= 16 + 12 -2 = 26

Using the t-distribution table, the critical value for t(0.025, df = 26) is equals to the 2.06. Now, the observed t-value = 0.91 is less than 2.06 ( standard t value), so, we do not reject H₀ . Hence, no evidence to support the researcher claim.

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Answer:

The probability of pulling a blue marble from the bag is;

Explanation:

Given that there are 2 blue, 5 yellow, and 3 white marbles in a bag.

The total number of marbles in the bag is;

The probability of pulling a blue marble from the bag will be;

Substituting the given values;

Therefore, the probability of pulling a blue marble from the bag is;

A distribution that has both mean and median of (-15) is referred to as a perfectly symmetrical distribution.

This is referred to as a type of distribution in which the values of the mean and the median are the same as they are the central component of inferential statistics.

In this scenario, we were given the mean and median to be of the same value which is (-15) which therefore denotes that the type of distribution is a perfectly symmetrical one.

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Answer:

Let the smaller integer be x and greater integer be (x+1)

x+(x+1)=91

2x+1=91

2x=91-1=90

x=90/2

x=45

Answer:

The integers are 45 and 46.

Step-by-step explanation:

Let the two consecutive integers be x and therefore the other will be x+1.

Given that the sum of the integers is 91.

So ATP,

Solving for first number i.e. x,

Hence,the first number is 45.

\(\rule{225pt}{2pt}\)

Solving for second number,i.e. x+1:

It can easily be obtained by substituting the value of x we got.

Hence,the second number is 46.

\(\rule{225pt}2pt\)

Answer: Option (4)

Step-by-step explanation:

We need factors of \((x+2), (x+1), (x-4)\)

Three methods for determining the volume of geometric shapes are the formula method, the displacement method, and the integral method.

The formula method is commonly used for basic geometric shapes such as cubes, rectangular prisms, cylinders, and spheres. These shapes have well-defined formulas for calculating their volumes, such as V = l x w x h for a rectangular prism or V = πr²h for a cylinder. This method is straightforward and easy to use, but it may not be applicable to irregular or complex shapes.

The displacement method involves immersing the shape in a liquid and measuring the amount of liquid displaced. The volume of the shape is then equal to the volume of the liquid displaced. This method is useful for irregular shapes that cannot be easily measured using traditional formulas. However, it requires careful measurements and may not be practical for large or delicate objects.

The integral method is a mathematical technique that uses calculus to determine the volume of a shape. It is particularly suited for complex three-dimensional objects that cannot be easily measured or calculated using other methods. By breaking down the shape into infinitesimally small elements and integrating their volumes, the total volume of the shape can be accurately determined. This method is highly precise but requires advanced mathematical knowledge and computational tools.

In conclusion, while the formula method and the displacement method are useful for simple and irregular shapes respectively, the integral method is expected to be the most precise for determining the volume of geometric shapes. It can handle complex shapes and provide accurate results, albeit requiring advanced mathematical skills and tools.

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Based on the given α (0.01) and p-value (0.001) pair, the correct conclusion is B. Reject the null hypothesis since the p-value is less than the value of α.

The p-value represents the probability of obtaining a test statistic as extreme or more extreme than the observed result, assuming the null hypothesis is true. It measures the strength of evidence against the null hypothesis.

In hypothesis testing, if the p-value is less than the chosen significance level (α), it indicates that the observed result is statistically significant. The significance level (α) is the threshold used to determine whether to reject or fail to reject the null hypothesis.

In this case, the p-value (0.001) is less than the significance level α (0.01). Since the p-value is smaller than α, it means that the observed result is highly unlikely to occur by chance under the assumption of the null hypothesis being true. Therefore, the correct conclusion is to reject the null hypothesis (option B).

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Answer:

D. 4.5

Step-by-step explanation:

<3

Answer:the answer will be D)4.5

Step-by-step explanation:

Answer:

-11y^5+2x

Step-by-step explanation:

subtract 3y^5 from -8y^5