The graph shows the grams of protein in different amounts of milk.

Which of these statements is true?

Math item stem image
CLEAR CHECK

There are 20 grams of protein in 2 cups of milk.


There are 8 grams of protein per cup of milk.


The unit rate of protein in milk is 13.5 grams per cup.


There are 1.5 grams of protein in 12 cups of milk.

The value of ㏒₁₀√3 - 1 / 2 ㏒₁₀2 is 1 / 2.㏒₁₀(1.5)

Given: To evaluate ㏒₁₀√3 - 1 / 2 . ㏒₁₀2

What are logarithms?

If a equation is given in the form of aᵇ = c, then ㏒ₐc = b or in a definitive way a logarithm is the power to which a number must be raised in order to get a number. As here 'a' is raised to the power 'b' to given a number c, so the number base 'a' if be raised to some power of 'b' then it will yield a number 'c'.

For example, 10² = 100 which can be written as ㏒₁₀100 = 2 by the following property of logarithm that is ㏒ₐ(bⁿ) = n.㏒ₐb.

So,  ㏒₁₀100 = ㏒₁₀10² = 2.㏒₁₀10 = 2 [ Another property ㏒ₐa = 1]

Some basic properties on logarithm operations are

1) ㏒ₙa + ㏒ₙb = ㏒ₙ(ab)

2) ㏒ₙa - ㏒ₙb = ㏒ₙ(a / b) [NOTE: ㏒ₙa - ㏒ₙb is not commutative]

3) ㏒ₐ(bⁿ) = n.㏒ₐb

4) ㏒ₐa = 1

Now let's solve the sum: ㏒₁₀√3 - 1 / 2 ㏒₁₀2

㏒₁₀√3 - 1 / 2 ㏒₁₀2 = ㏒₁₀(3)\(^{\frac{1}{2}}\) - 1 /2 .㏒₁₀2 [ Root means 1 / 2 power]

= 1 / 2.㏒₁₀(3) - 1 / 2.㏒₁₀(2)   [ ㏒ₐ(bⁿ) = n.㏒ₐb ]

= 1 / 2.(㏒₁₀(3) - ㏒₁₀(2))

= 1 / 2.(㏒₁₀(3 / 2)                  [ ㏒ₙa - ㏒ₙb = ㏒ₙ(a / b) ]

= 1 / 2.㏒₁₀(1.5)

Hence value of ㏒₁₀√3 - 1 / 2 ㏒₁₀2 = 1 / 2.㏒₁₀(1.5)

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Answer:

17,100

Step-by-step explanation

The hundreds place in the number is 113, if you round 113 you get 100 because it is closer to 100 than it is to 200

Answer:

25.7

Step-by-step explanation:

Hope this helps.

Answer:

25 2/3

Step-by-step explanation:

On solving the provided question, we can say that in the provided rectangle the fence is 14 m wide.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

provided

let length will be = 3w

width = w

perimeter of rectangle = 2(l+b) = 2(3w+w) = 8w

8w = 120

w = 14

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Answer:

120 cars

Step-by-step explanation:

The given function is

\(C(x)=0.5x^2-120x+21,481\)

and its parent function would be

\(f(x)=ax^2+bx+c\)

So,

\(a=0.5\)

\(b = -120\)

and

\(c = 21,481\)

The minimum cost would be found using:

\(x = -\frac{b}{2a}\)

So just input a and b into the function:

\(x= -\frac{-120}{2(0.5)}\)

\(x=-\frac{-120}{1}\)

\(x = 120\)

Therefore there must be 120 cars made to minimize the cost.

Answer: 7.2

Step-by-step explanation: 2.4(3) is really just 2.4 * 3 so 2.4 times 3 is 7.2.

Answer:

13.824

Step-by-step explanation:

Raise 2.4 to the power of 3.

Answer:

Shama types at a constant rate she types 12 letters in 4 seconds what is the constant of proportionality for the relationship of letters to minutes

Answer choices

3

48

180

2,880

Help I need this answer fast I’m taking a test and I can’t fail 7th grade

Step-by-step explanation:

Shama types at a constant rate she types 12 letters in 4 seconds what is the constant of proportionality for the relationship of letters to minutes

Answer choices

3

48

180

2,880

Help I need this answer fast I’m taking a test and I can’t fail 7th grade

The constant of proportionality for the relationship of letters to minutes is 180.

Two set of quantities are said to be directly proportional or just simply proportional if the corresponding elements of these two sets has a constant ratio. This constant is called the proportionality constant or coefficient of proportionality.

We have the proportional relationship between letters typing and the time in minutes taken to type the letters.

Time taken by Shama to type 12 letters = 4 seconds

                                                                  = 4 / 60 minutes

                                                                  = 1/15 minutes

Proportionality constant can be found by taking the ratio of these quantities.

That is, proportionality constant = 12 / (1/15)

The fraction in the denominator will be taken to the numerator as the reciprocal and the operation changes into multiplication.

Proportionality constant = 12 × (15/1) = 180

Hence the proportionality constant for the relationship of the quantities letters and minutes is 180.

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Answer: 6

Step-by-step explanation: 288

=

3

(

4

)

×

w

×

4

w

=

288

3

(

4

)

⋅

4

=

72

12

=

6

I think <3

Answer:

The width is  

6  cm. You can find it by taking the formula for the volume of a cube and rearranging it to find the width.

Step-by-step explanation:

Answer:

a = -3 and b = 1

Step-by-step explanation:

x² - 6x + 10

→ Half the second term and place it in the bracket

( x - 3 )²

→ Square -3

- ( 3 )² = -9

→ Place this outside the brackets along with plus 10

( x - 3 ) ² - 9 + 10

→ Simplify

( x - 3 ) ² + 1

Answer:

yor answer is 52

Step-by-step explanation:

it can be concluded that the population standard deviation is within or less than 12.

To construct a hypothesis test to determine whether the population standard deviation of σ≦12 should be rejected for Costco, we can use a chi-square test for variance.

Step 1: State the null and alternative hypotheses:
- Null hypothesis (H₀): σ ≤ 12
- Alternative hypothesis (H₁): σ > 12

Step 2: Determine the level of significance (α = 0.05) and degrees of freedom (df = n - 1 = 11 - 1 = 10).

Step 3: Calculate the test statistic:
- χ² = (n - 1) * (s² / σ²) = 10 * (11.3² / 12²) = 10 * 0.94 = 9.4

Step 4: Determine the critical value:
- The critical value at α = 0.05 with df = 10 is χ²ₐ = 18.307

Step 5: Compare the test statistic with the critical value:
- Since χ² = 9.4 < χ²ₐ = 18.307, we fail to reject the null hypothesis.

Step 6: Conclusion:
- Based on the given sample data, there is not enough evidence to reject the hypothesis that the population standard deviation of σ≤12 for Costco.

Therefore, it can be concluded that the population standard deviation is within or less than 12.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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Answer:

-0.5 is not a solution

2 is a solution

Step-by-step explanation:

To check if something is a solution of the equation, you need to substitute the value in place of the variable

15 + 2y = -12 - 4y

15 + 2(-0.5) = -12 - 4(-0.5)

15 - 1 = -12 + 2

14 ≠ -10 ∴ -0.5 is not a solution

5 - 2(3x + 5) = 3 - 10x

5 - 2[3(2) + 5] = 3 - 10(2)

5 - 2(6 + 5) = 3 - 10(2)

5 - 12 - 10 = 3 - 120

-17 = -17 ∴ 2 is a solution

Answer:

-2(2+5r)

Step-by-step explanation:

-(7+10r)+3

then you remove the parentheses

-7-10r+3

calculate the sum

-4-10r

factor the expression

-2(2+5r)

Answer:-1

Step-by-step explanation:

Answer: -6

Step-by-step explanation:

the line pass through (-3,-6)

The algebraic expression in simplest terms is 200 · x² - 79 · x + 14 = 0.

In this problem we have a sum of products of binomials as algebraic expression and we must reduce to its simplest terms by using algebra properties, that is, using these properties until a polynomial is found:

(- 10 · x + 2) + (- 9 · x + 8) · (- 10 · x + 2) + (- 9 · x + 8) · (- 10 · x + 2) + (- 9 · x + 8)

(- 10 · x + 2) + 2 · (- 9 · x + 8) · (- 10 · x + 2) + (- 9 · x + 8)

(- 10 · x + 2) · [1 + 2 · (- 10 · x + 2)] + (- 9 · x + 8)

(- 10 · x + 2) · (1 - 20 · x + 4) + (- 9 · x + 8)

(- 10 · x + 2) · (3 - 20 · x) + (- 9 · x + 8)

3 · (- 10 · x + 2)  + (- 20 · x) · (- 10 · x + 2) + (- 9 · x + 8)

- 30 · x + 6 + 200 · x² - 40 · x - 9 · x + 8

200 · x² - 79 · x + 14

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Answer:

48...boys will be 28 and girls will be 20

Answer: 48 people in total

Step-by-step explanation:

If the ratio is 7 boys per 5 girls and in the real situation there is a difference of 8 boys then we can do some equivalent ratios.

- times 2:

7*2=14

5*2=10

so, 14 per 10 is one, however, it hasn't a difference of 8. Since 14-10=4.

If the difference is 4 and we need a difference of 8 we can multiply by 2. So, now we can make an equivalent ratio multiplied by 4, because 2 * 2 =4

- times 4:

7*4=28

5*4=20

So, 28 boys per 20 girls is the correct answer. There are 48 people in total:)

According to the discount, the price of the tablet computer after the markup is $610.30.

In this problem, a store offered a 30% discount on a tablet computer that originally sold for $670. We can calculate the discounted price of the tablet computer by finding 30% of its original price and subtracting it from the original price.

Discounted price = Original price - Discount

Discounted price = $670 - 30% of $670

Discounted price = $670 - $201

Discounted price = $469

So, the discounted price of the tablet computer is $469.

The problem then asks us to find the price of the tablet computer after it is marked up by 30%. To do this, we need to add 30% of the discounted price to the discounted price.

Markup price = Discounted price + Markup

Markup price = $469 + 30% of $469

Markup price = $469 + $141.30

Markup price = $610.30

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Answer:

Something that's in your budget.

(a) The seven consecutive numbers are \(n,n+1,n+2,n+3,n+4,n+5,n+6\).

(b) The sum of all the seven consecutive numbers is \(7n+21\).

Given:

The smallest number in the seven consecutive numbers is \(n\).

Explanation:

(a)

The gap between two consecutive numbers is always \(1\). It means we can add \(1\) in the current number to get the next number.

First number is \(n\), so the second number is \(n+1\) and the third number is \((n+1)+1\) that is \(n+2\).

Fourth number: \((n+2)+1=n+3\)

Fifth number: \((n+3)+1=n+4\)

Sixth number: \((n+4)+1=n+5\)

Seventh number: \((n+5)+1=n+6\)

Therefore, seven consecutive numbers are \(n,n+1,n+2,n+3,n+4,n+5,n+6\).

(b)

The sum of these seven consecutive numbers is:

\(\text{Sum}=n+(n+1)+(n+2)+(n+3)+(n+4)+(n+5)+(n+6)\)

\(\text{Sum}=(n+n+n+n+n+n+n)+(1+2+3+4+5+6)\)

\(\text{Sum}=7n+21\)

Therefore, the sum of all the seven consecutive numbers is \(7n+21\).

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The amount that a $90,000 loan cost Lauren than Demarcus will be $8280.

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

From the information, Demarcus and Lauren each take out a $90,000 loan for a new condo and each has to repay the loan in 10 years. It should be noted that 10 years in months will be:

= 10 × 12 = 120 months

The difference in the amount paid as a result of the credit score will be:

= ($840 × 120) - ($771 × 120)

= $100800 - $92520

= $8280

Therefore, the amount is $8280.

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Use the CSS "background-image" property to configure a linear gradient.

The "background-image" property in CSS allows you to set an image or a gradient as the background of an element. When configuring a linear gradient, you can use the "linear-gradient()" function as the value for the "background-image" property. This function allows you to define the starting and ending points of the gradient, as well as the colors and stops along the gradient.

By specifying the desired colors, positions, and angles within the "linear-gradient()" function, you can create customized linear gradients to apply as backgrounds to elements on a web page, achieving visually appealing effects and smooth transitions.

Therefore, Use the CSS "background-image" property to configure a linear gradient.

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To configure a linear gradient in CSS, you can use the 'background-image' property with the 'linear-gradient()' function.

To configure a linear gradient in CSS, you can use the 'background-image' property along with the 'linear-gradient()' function. Here's an example:

In the above code, replace 'element' with the selector for the HTML element you want to apply the gradient to. 'direction' specifies the direction of the gradient, such as 'to right' or 'to bottom'. 'color1', 'color2', and so on represent the colors you want to use in the gradient. You can specify multiple colors to create a smooth transition between them.

For example, to create a horizontal gradient from red to blue, you can use the following code:

This will apply a linear gradient from red to blue horizontally on the selected element.

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Answer:wow this is hard

Step-by-step explanation:

Answer:

38 students are not in the art club while 12 student are in the art club.

Step-by-step explanation:

Percent I am not exactly sure, I'm sorry, still I hope this somehow helped!

The cost of each t-shirt is $7, using the equation formed from the given conditions.

In the question, we are given that the drama club is printing t-shirts for its members. The printing company charges a certain amount for each shirt plus a setup fee of $40.

We are aske to find the cost of each t-shirt if there are 21 students in the club and the t-shirt order costs a total of $187.

We assume the cost of one t-shirt to be $x.

Thus, the cost of printing 21 t-shirts = $21x.

The setup fee is given to be $40.

Thus, the total cost of printing 21 t-shirts for the dram club = $21x + 40.

But, we are given that the total cost is $187.

Thus, we get an equation,

21x + 40 = 187.

This equation can be solved as follows:

21x + 40 = 187,

or, 21x = 187 - 40,

or, 21x = 147,

or, x = 147/21,

or, x = 7.

Thus, the cost of each t-shirt is $7, using the equation formed from the given conditions.

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a) The first neglected term in the series is \((1/16)(0.4)^7 = 3.3\times 10^-7\), which is smaller than the desired error of\(5 \times 10^-6\).

b) The first neglected term in the series is\((1/384)(0.5)^8 = 1.7\times10^-5,\)which is smaller than the desired error of 0.001.

a) To approximate the integral ∫\(0.4√(1+x^2)dx\) with an error of less than \(5x10^-6\), we can use a Taylor series expansion centered at x=0 to approximate the integrand:

√(\(1+x^2) = 1 + (1/2)x^2 - (1/8)x^4 + (1/16)x^6 -\) ...

Integrating this series term by term from 0 to 0.4, we get an approximation for the integral with error given by the first neglected term:

\(I = 0.4 + (1/2)(0.4)^3 - (1/8)(0.4)^5 = 0.389362\)

b) To approximate the integral ∫\(0.5x^3e^-x^2dx\) with an error of less than 0.001, we can use a Maclaurin series expansion for \(e^-x^2\):

\(e^-x^2 = 1 - x^2 + (1/2)x^4 - (1/6)x^6 + ...\)

Multiplying this series by \(x^3\) and integrating term by term from 0 to 0.5, we get an approximation for the integral with error given by the first neglected term:

\(I = (1/2) - (1/4)(0.5)^2 + (1/8)(0.5)^4 - (1/30)(0.5)^6 = 0.11796\)

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Answer:

c

Step-by-step explanation:

the second triangles dimensions are 1.5 times greater than the first one.

Therefore (b). A chi-square statistic is always positive as it is the sum of squared deviations from expected values.

However, it can contain fractions or decimal values as it is based on continuous data. The chi-square distribution is skewed to the right and its shape depends on the degrees of freedom. The possible values for a chi-square statistic depend on the sample size and the number of categories in the data. In general, larger sample sizes and more categories will result in larger chi-square values. It is important to note that a chi-square statistic cannot be negative as it is the sum of squared deviations. Therefore, options (a) and (c) are incorrect. In conclusion, the correct answer is (b) and it is important to understand the properties and interpretation of chi-square statistics in statistical analysis.

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The number  \(log_2^3\) is an irrational number.

For given question,

We need to prove \(log_2^3\) is an irrational number.

An irrational number is a real number x that cannot be written as the ratio of two integers.

Assume that \(log_2^3\) is rational.

⇒ \(log_2^3\) = a/b

where a and b are positive integers with no factor in common.

Then  3 = \(2^{(\frac{a}{b} )}\)

or

\(3^b=2^a\)

which is impossible since 3^(b) is odd and 2^(a) is even.

Hence \(log_2^3\) cannot be rational, that is it is irrational.

Therefore,  \(log_2^3\) is an irrational number.

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