Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut butter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn’t think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.

The equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

Here, we are given a circle with center D and equation as-

[tex]x^{2}+ y^{2}+2x -8y + 8 =0[/tex]

Comparing this to the general form of equation of a circle which is  [tex]x^{2}[/tex] + [tex]y^{2}[/tex]+ 2gx + 2fy + c = 0, we get-

g = 1, f = -4 and c = 8

thus, the center of the circle is (-1,4) and radius =[tex]\sqrt{ (1+16-8)}[/tex] = 3

Now, since PT is a tangent to the circle, DP will e perpendicular to PT.

We can find the length of PD using the distance formula as we know P(4,6) and D(-1,4)

= [tex]\sqrt{(4+1)^{2} +(6-4)^{2} }[/tex]

= [tex]\sqrt{(5)^{2} +(2)^{2} }[/tex]

= [tex]\sqrt{25 +4 }[/tex]

=[tex]\sqrt{29}[/tex]

Thus, in triangle, PDT by using Pythagoras theorem, we will have-

[tex]PT^{2} + DT^{2} = PD^{2}[/tex]

since DT is the radius of the circle, DT = 3

⇒ [tex]PT^{2} + 3^{2} = (\sqrt{29}) ^{2}[/tex]

[tex]PT^{2} + 9 = 29[/tex]

[tex]PT^{2} = 29 - 9[/tex]

[tex]PT^{2} = 20[/tex]

[tex]PT = \sqrt{20}[/tex]

Thus, we've proved that the length of PT is [tex]\sqrt{20}[/tex] units.

Now, the circle with center P, passing through T will have radius = [tex]\sqrt{20}[/tex]

so r = [tex]\sqrt{20}[/tex] and (h,k) = (4,6)

Thus, the equation of the circle will be-

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]

[tex](x-4)^{2} + (y-6)^{2} = (\sqrt{20}) ^{2}[/tex]

[tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

Thus, the equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

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The sum of the first 31 terms of the arithmetic series is 114.

What is arithmetic series?

In mathematics, arithmetic series is the sequence of the number whose common difference between the two consecutive number is always constant. And the sum of the series is depend on the first term as well as on the last term.

According to the question, the given series is an arithmetic series. In the common difference is same.

The given series is:

4, 11, 18,....4, 11, 18,....4, 11, 18,....

To know the sum of the given series, first calculate the sum of the first three numbers. And later multiply by ten.

Using standard formula for the sum of the arithmetic series:

[tex]S_{3} =\frac{(first term + last term)}{2} = \frac{4+18}{2} =11[/tex]

Therefore to calculate the sum of the 31 terms:

s(31 terms) = 10(11) + first term = 110 + 4 = 114

Hence, the sum of the first 31 terms of the arithmetic series is 114.

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1) Let's solve that exponential equation

Converting the bases:

2) Since we are on the same base let's just calculate the exponents.

3) Blake has committed a mistake when He didn't apply the distributive property properly. He didn't multiply the 7 by 4. He subtracted the x variables wrongly and added -7 to -5.

When He started operating the exponents.

To write  3.656 X 10^-5 in standard form 0.00003656

What is Standard Form ?

A mathematical item's canonical, normal, or standard form refers to how the object is typically expressed mathematically in both mathematics and computer science. It is frequently the one that offers the most straightforward illustration of the thing while yet enabling distinctive identification.

Move the decimal in the number that many spaces to the right when multiplying a number by 10 to the power of a positive exponent

(for example, (10)^3)).

For example, 4.5x(10)^3=4500.

Move the decimal in the number (the absolute value of) that many spaces to the left when multiplying a number by 10 to the power of a negative exponent

(for example, (10)^4)).

For example, (4.5x10)^4=(0.00045)

Move the decimal five spaces to the left for (3.656x 10)^-5:

0.00003656

Hence , 0.00003656 is Standard form of  (3.656x 10)^-5

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Using the z-distribution to test the hypothesis, we have that:

a) The null hypothesis is [tex]H_0: \mu = 50[/tex].

b) The p-value of the test is greater than 0.05, hence we do not reject the null hypothesis, meaning that the supplements did not have the intended effect.

At the null hypothesis, it is tested if there is not enough evidence that the mean was different, hence:

[tex]H_0: \mu = 50[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the mean was different, hence:

[tex]H_1: \mu \neq 50[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

In the context of this test, the parameters are given as follows:

[tex]\overline{x} = 54, \mu = 50, \sigma = 12, n = 16[/tex]

Hence the test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{54 - 50}{\frac{12}{\sqrt{16}}}[/tex]

z = 1.33.

Considering a two-tailed test, as we are testing if the mean is different of a value, with z = 1.33, the p-value of the test is of 0.1835, which is greater than 0.05, meaning that we do not reject the null hypothesis and the supplement did not change the mean.

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When we write an inequality in the form:

In a number line, we can draw it, mark the endpoints (1 and 5) and then we highlight the parts at which the x is, which is in the middle:

Notice that we marked the endpoints as empty dots, which indicates that the endpoints are not included in the interval.

The most appropriate choice for linear equation will be given by-

The cost of bench is $375

What is linear equation?

A one degree equation is called a linear equation.

Here,

Let the cost of the bench be $x

cost of garden table = $(x + 80)

Total cost of bench and garden table= $(x + x + 80)

                                                              = $(2x + 80)

By the problem,

                           2x + 80 = 830

                            2x = 830 - 80

                             2x = 750

                                x = [tex]\frac{750}{2}[/tex]

                                x  = $375
So,

The cost of bench is $375

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Check the picture below.

let's bear in mind that the standard deviation measures deviation in a dataset, so is a measure of how much the data fluctuates, so a dataset of 3 , 1000, will have a much higher deviation value than a same total of 450 , 553.

An equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) = 72.2 .

As given in the question,

Pierce is making a rectangular frame for a photo collage.

Perimeter of a rectangular frame is equal to 72.2 inches.

Length of the rectangular frame is equal to 20.3 inches

Perimeter of the rectangle = 2(length + width) __(1)

Let x inches be the width of the frame

Equation with x width of the frame is given

2(20.3 + x) = 72.2

Therefore, an equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) =72.2.

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SOLUTION

Given the question in the image, the following steps can be used to get x

Step 1: Explain the concept of equal arcs in a circle

If a circle is divided into arcs, then each arc is a minor arc and they all sum up to be equal to the total angles in the circumfference of the circle which is 360 degrees.

Step 2: Explain the breakdown of the minor arcs in the circle

It can be seen that the minor arcs divided the circle into three parts which are two equal arcs and a 70 degrees arc. This implies that:

Step 3: Find x

Hence, the value of x in the given circle is 145 degrees

Answer:2 choice

Step-by-step explanation:you use the rise over run technique with 2 points, it should give you rise 1 run 4 since the line is decreasing its a negative. For the y-int its the point where the line crosses Y int which is (0,-2) answer is -2

The cost of the present is $20.67

Given,

The cost of the present = x

Amount given by cousin = $13.78

Amount given by cousin is 2/3 of x.

That is,

13.78 = 2/3 of x

Lets find x

13.78 = 2/3 × x

13.28 = 2x/3

Multiply with 3 on both sides

13.78 × 3 = (2x/3) × 3

We get,

41.34 = 2x

Divide 2 on both sides

That is,

41.34/2 = 2x/2

We get,

x = 20.67

Here, x is the cost of the present

Therefore, the cost of the present is $20.67

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Answer:

[tex]{ \tt{\% savings = \frac{savings}{total \: income} \times 100\%}} \\ \\ { \tt{ = \frac{720}{3000} \times 100\%}} \\ \\ = { \tt{24\%}}[/tex]

Answer:

24%

Step-by-step explanation:

[tex]\boxed{\sf Percent=\left(\dfrac{Value}{Total\:value}\right) \times 100}[/tex]

Given information:

Substitute the given values into the formula and solve for percent:

[tex]\begin{aligned}\implies \textsf{Percent} & =\dfrac{720}{3000} \times 100\\\\& = \dfrac{720\times 100}{3000} \\\\& = \dfrac{72000}{3000} \\\\& = \dfrac{72}{3} \\\\& = 24\% \end{aligned}[/tex]

Therefore, 24% of Tanisha's budget is savings.

The three Points that  lie on the given line 2x=6y+4 are  (5,1) , (8,2) and (11,3).

The given equation of line is given below,

2x=6y+4                              equation 1

We need to find the points that lie on the given line.

Point 1 :

Put x = 5 in equation 1

2(5) = 6y + 4

6y = 6

y=1

So, Point (5,1) lie on the given line.

Point2:

Put x = 8 in equation 1

2(8) = 6y + 4

6y = 12

y=2

So, Point (8,2) lie on the given line.

Point 3 :

Put x = 11 in equation 1

2(11) = 6y + 4

6y = 18

y=3

So, Point (11,3) lie on the given line.

Thus, Points (5,1) , (8,2) and (11,3) lie on the line 2x=6y+4 .    

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The value of k given that both points lie on a line passing through the origin is 48.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Since both points lie on a line which passes through the origin, we can logically deduce the following points:

Point (x, y) = (0, 0)

Substituting the given points into the formula, we have;

Slope, m = Δy/Δx

Slope, m = (-2 - 0)/(-12 - 0)

Slope, m = -2/-12

Slope, m = 1/6

At point (-12, -2) and (k, 8), we have:

1/6 = (8 - (-2))/(k - (-12))

1/6 = (8 + 2)/(k + 12)

1/6 = 10/(k + 12)

k + 12 = 10(6)

k + 12 = 60

k = 60 - 12

k = 48

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Answer:

  1.1

Step-by-step explanation:

You want the multiplier of the wholesale cost that makes the retail cost be 10% more.

The retail cost is said to be ...

   retail cost = (wholesale cost) + 10% × (wholesale cost)

  = (wholesale cost) × (1 +10%)

  = (wholesale cost) × 1.10

The retail cost is 1.10 times the wholesale cost.

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Answer: B. (5√3)

Step-by-step explanation: In a 60-30-90 triangle, the hypotenuse is 2x, and the long is x√3. Solve for x by setting 2x=10, which you would get 5. Then, you can plug 5 for x in x√3 to get 5√3.

Answer:900

Step-by-step explanation: 1. set up an equation

x= (p * n)/100 when x= the answer p= the percentage and n= the total number

2. plug in the numbers

x= (30 * 3000)/100

3.solve

x= (30*3000)/100

x= (90000)/100

x= 900

Total expenses = $289 + $361 + $433 + $217 = $1300

Percentage of money spent on rent:

(Money spent on rent)/(Total expenses) = $361/$1300 = 0.2777 ≈ 28%

Therefore 28% of total expenses are for rent

    Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.

How to determine a line's equation from two points:

Using the slope formula, determine the slope.

To find the y-intercept (b), use the slope and one of the points.

You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).

y = -x/3 + 5 is the equation that depicts the line that crosses through the coordinates (-6, 7) and (-3, 6).

3 Answers What is the slope of the line passing through (- 7 2 and 6 7? by Certified Tutors

The slope of the equation would be nine.

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The diagram of the number line is shown below

Thus, the distance CD which is the distance between point D and point C is

13 - 11 = 2

CD = 2

The liters of 80% material is 2/3 liters.

The liters of the 50% solution is 1/3 liters.

Based on the information, the scientist is working with two different concentrations of hydrochloric acid (HCI).

Let x = volume of 80%

Let 1 -x =volume of 50%

Therefore, the expression to illustrate the information will be:

80x + 50 × (1 - x) = 70

80x + 50 - 50x = 70

30x = 70 - 50

30x = 20

Divide

x = 20/30

x = 2/3

Therefore there are 2/3 liters of 80% material

The liters for the 50% solution will be 2/3 subtracted from 1. The 2/3 implies that for the 80% material. This will be:

= 1 - 2/3

= 1/3

There are also 1/3 liters of 50% material.

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The difference between the depths in February and July is D. 13 feet.

From the information illustrated, it was stated that the depth of a local lake average 26 ft is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|.

Therefore, it should be noted that the depth in July is -18.

Therefore, the difference between the depths in February and July will be:

= -5 - (-18)

= -5 + 18

= 13

Therefore, the difference is 13 feet.

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Steve's new credit card balance at the end of the month and after making the minimum monthly payment will be $519.39.

A credit card balance is an amount the cardholder owes to the credit card issuer at the end of a credit period.

The credit card balance consists of purchases, finance charges, and repayments.

Credit card's APR = 11.99%

Credit limit = $1,800

Minimum monthly payment = 6.5%

Purchase at the beginning of the month = $550

Credit card interest for the month = $5.50 ($550 x 11.99% x 1/12)

New balance = $555.50

Minimum payment = $36.11 ($555.50 x 6.5%)

Balance after the minimum payment = $519.39 ($555.50 - $36.11)

Thus, If he buys $550 in school supplies at the beginning of the month, Steve’s new balance at the end of the month is $555.50, which he can reduce to $519.39 by making the required minimum monthly payment.

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For the given problems we have:

1) The solution of the inequality is:

x ≤ 2

2) The absolute value equation has two solutions:

z= 2

z = -12

3) The correct matches are:

Remember that solving means to isolate the variable in one side of the expression.

1) We have the inequality:

-4x + 17 ≥ 9

-4x  ≥ 9 - 17

x ≤ -8/-4

x ≤ 2

This is the solution of the inequality.

2) We have the absolute value function:

|5 + z| + 3 = 10

|5 + z| = 10 - 3 = 7

We can decompose this into:

5 + z = 7

5 + z = -7

Then the two solutions are:

z = 7 - 5 = 2

z = -7 - 5 = -12

3) The correct matches here are:

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We are to solve using completing the square:

1/4x² + x + 1/4 = 0

Let's collect like terms:

1/4x² + x = -1/4

Divide both sides by the coefficient of x-squared:

x² + 4x = -1

Take half of the coefficient of x, square it, then add to both sides:

x² + 4x + 4 = -1 + 4

factor the left side of the equation:

(x + 2)² = 3

Take the root of both sides;

x + 2 = ±√3

Add 2 to both sides:

x = ±√(3) - 2

x = -2 + √3 or x = -2 - √3

herefore, the correct option is B, which is x = -2 + √3 or x = -2 - √3