Each week, Diana spends 4 hours playing soccer and 6 hours babysitting. Which ratio is equivalent to the ratio of the time Diana spends playing soccer to the time she spends babysitting?
To find a baseball pitcher's earned run average (ERA), you can use the formula Ei=9r, where E represents ERA, i represents number of innings pitched, and r represents number of earned runs allowed. Solve the equation for E ...?
Answer:
[tex]E=\frac{9r}{i}[/tex]
Step-by-step explanation:
We have been given an equation [tex]Ei=9r[/tex], where [tex]E[/tex] represents ERA, [tex]i[/tex] represents number of innings pitched, and [tex]r[/tex] represents number of earned runs allowed.
To solve the given equation for [tex]E[/tex], we need to separate [tex]E[/tex] on one side on equation.
To separate [tex]E[/tex] on one side on equation, we will divide both sides of equation by [tex]i[/tex].
[tex]\frac{Ei}{i}=\frac{9r}{i}[/tex]
[tex]E=\frac{9r}{i}[/tex], where [tex]i\neq 0[/tex]
Therefore, our required equation would be [tex]E=\frac{9r}{i}[/tex].
sketch the graph of each linear inequality y>-2x-2
To sketch the graph of the inequality y > -2x - 2, draw a dashed line for y = -2x - 2 and shade the area above this line, as this area represents the solution set of the inequality.
Explanation:To sketch the graph of the linear inequality y > -2x - 2, you would begin by drawing the line y = -2x - 2 as if it were an equation. This line serves as the boundary between the solutions of the inequality and the non-solutions. Since the inequality is greater than, not greater than or equal to, you'll use a dashed line to indicate that points on the line are not included in the solution set.
Next, since the inequality is y > -2x - 2, you will shade the area above the line to indicate that all the points in this area satisfy the inequality. That shaded region represents all the possible solutions to the inequality. Always remember when graphing inequalities to pick a point, often(0,0) if it's not on the line, and check if it satisfies the inequality to ensure correct shading area.
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Explane how you can tell 4 is a factor of 30
I need help photo attached
What is 15 divided by 1,230?
Find the product of (3x + 7y)(3x − 7y).
9x2 − 42xy + 49y2
9x2 + 42xy + 49y2
9x2 − 49y2
9x2 + 49y2 ...?
The correct answer for the product of [tex](3x+7y)(3x-7y)[/tex] is [tex]9x^2+49y^2[/tex].The correct option is [tex]b.[/tex].
Given expression:
[tex](3x+7y)(3x-7y)[/tex]
To simplify multiply first term and second term of first expression with second expression separately:
Simplify:
[tex]3x(3x+7y)+7y(3x-7y)[/tex]
[tex]= 9x^2+21xy +21xy-49y^2[/tex]
Add Like terms:
[tex]= 9x^2+42xy-49y^2[/tex]
The product of [tex](3x+7y)(3x-7y)[/tex] is [tex]= 9x^2+42xy-49y^2[/tex] . The correct option is [tex]b.[/tex]
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Which of the point-slope equations below is correct for the line that passes through points (-4,-4) and (1,3)? Check all that apply.
A. y - 3 = 7/5(x - 1)
B. y - (-4) = 7/5(x - (-4))
C. y - 3 = 7/5(x + 1)
D. y + 4 = 7/5(x - 4)
E. y + 4 = 7/5(x + 4)
F. y + 4 = 5/7(x + 4)
Find the value of x. Round the answer to the nearest tenth, if needed.
A.
9
B.
18.9
C.
22
D.
32.1
Ethan's club spent $81 for 9 caps for its members each cap cost the same amount how much did each cap cost
Emily has a coupon for 20% off her purchase. She finds a backpack on the discount rack. It's original price is $60 but is 30% off.
Emily thinks 30% & 20 % make 50% so the backpack will be $30.
Is Emily correct? Explain your answer.
What is the sum of the polynomials?
(–x2 + 9) + (–3x2 – 11x + 4)
–4x2 – 2x + 4
–4x2 – 11x + 13
2x2 + 20x + 4
2x2 + 11x + 5
For this case we have the following polynomials:
[tex] -x ^ 2 + 9
-3x ^ 2 - 11x + 4
[/tex]
Adding the polynomials we have:
[tex] (-x ^ 2 + 9) + (-3x ^ 2 - 11x + 4)
[/tex]
Rewriting we have:
[tex] x ^ 2 (-1-3) - 11x + (9 + 4)
[/tex]
Therefore, the result of the sum is:
[tex] -4x ^ 2 - 11x + 13
[/tex]
Answer:
the sum of the polynomials is:
[tex] -4x ^ 2 - 11x + 13
[/tex]
option 2
A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle.
The first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. What is the equation for the situation, written in standard form?
A x2 – 99 = 0
B x2 – 99x = 0
C x2 + 5x + 104 = 0
D x2 + 5x – 104 = 0
The quadratic equation for the word problem, written in standard form is equal to: D. x² + 5x - 104 = 0.
Given the following data:
L = (W + 5) inches.
Area = 104 square inches.
Note: Let the width be x.
How to calculate the area.Mathematically, the area of a rectangle is calculated by using this formula:
LW = A
(x + 5)x = 104
x² + 5x = 104
x² + 5x - 104 = 0
In Mathematics, the standard form of a quadratic equation is given by ax² + bx + c = 0 ⇔ x² + 5x - 104 = 0.
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Name the set(s) of numbers to which 1.68 belongs.
none of the above
rational numbers, irrational numbers
rational numbers
natural numbers, whole numbers, integers, rational numbers
Answer:
The correct option is C) rational numbers
Step-by-step explanation:
Consider the provided number 1.68
Natural numbers: The natural numbers are 1, 2, 3, 4, 5,…
Whole number: Whole numbers are the set of natural numbers but starts with 0. i.e. 0, 1, 2, 3, 4, 5,…
Integers: Integers are the set of whole number and the negatives of the natural numbers, i.e, … ,-2, -1, 0, 1, 2, …
Rational number: A number is said to be rational, if it is in the form of p/q. Where p and q are integer and denominator is not equal to 0.
Irrational number: A number is irrational if it cannot be expressed be expressed by dividing two integers. The decimal expansion of Irrational numbers are neither terminate nor periodic.
Real numbers: All rational and Irrational numbers are called real number.
Now consider the provided number 1.68
The number has 2 digit after decimal point its means it is neither natural nor whole number, also it is not an integer.
The number 1.68 can be written in the form of p/q. Thus, it is a rational number.
As it is rational it can't be irrational. The number 1.68 is real number.
Hence, the correct option is C) rational numbers.
The table shows the amounts of food collected by two homerooms. Homeroom A collects 21 additional items of food. How many more items does Homeroom B need to collect to have more items per student Homeroom A Homeroom B
Students 24 16
Canned Food 30 22
Dry Food 42 24
The number of food items Homeroom B needs to collect to have more food items per student than Homeroom A is 16
How many more items does Homeroom B need to collect to have more items per student?Food items collected by homeroom A:
Canned food = 30
Dry food = 42
Additional food items = 21
Number of students = 24
Food items per students = (30 + 42 + 21) / 24
= 93/24
Food items collected by homeroom B:
Canned food = 22
Dry food = 24
Additional food items = x
Number of students = 16
Food items per students = (22 + 24 + x) / 16
= (46 + x) / 16
Number of more food items Homeroom B need to collect to have more items per student than Homeroom A:
(46 + x) / 16 > 93/24
cross product
(46 + x) × 24 > 16 × 93
1,104 + 24x > 1,488
24x > 1,488 - 1,104
24x > 384
Divide both sides by 24
x > 384/24
x > 16
Hence, homeroom B should collect more than 16 food item to have a greater item per student
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Homeroom B needs to collect at least 17 more items to exceed Homeroom A in items per student. The calculation is based on the total food items and the number of students in each homeroom.
To find out how many more items Homeroom B needs to collect to have more items per student than Homeroom A, we will first calculate the items per student for each homeroom, considering that Homeroom A collects 21 additional items.
First, calculate the total items of food collected by each homeroom:
Homeroom A:
- Canned food: 30 items
- Dry food: 42 items
- Additional items: 21 items
Total items for Homeroom A:
30 + 42 + 21 = 93 items
Number of students in Homeroom A: 24
Items per student in Homeroom A:
[tex]\[\frac{93}{24} \approx 3.875 \text{ items per student}\][/tex]
Homeroom B:
- Canned food: 22 items
- Dry food: 24 items
Total items for Homeroom B:
22 + 24 = 46 items
Number of students in Homeroom B: 16
Items per student in Homeroom B:
[tex]\[\frac{46}{16} = 2.875 \text{ items per student}\][/tex]
Determine additional items needed for Homeroom B:
Let ( x ) be the additional items needed for Homeroom B to exceed Homeroom A's items per student.
The new total items for Homeroom B would be:
46 + x
The new items per student for Homeroom B would be:
[tex]\[\frac{46 + x}{16}\][/tex]
We need this to be greater than Homeroom A's items per student:
[tex]\[\frac{46 + x}{16} > 3.875\][/tex]
Solving for ( x ):
46 + x > 3.875 × 16
46 + x > 62
x > 62 - 46
x > 16
Thus, Homeroom B needs to collect more than 16 additional items to have more items per student than Homeroom A.
In conclusion, Homeroom B needs to collect at least 17 more items to exceed Homeroom A in items per student.
when you shift shift a function, you are ____ it.
A. Moving
B. Stretching
C. Compressing
D. Flipping
Can you simplify 1/18
12 is what percent of 30
If the measure of angle 1 the measure of angle 2 = 180 and the measure of angle 3 the measure of angle 2 = 180 then the measure of angle 1 is congruent to angle 3 explain why its true
need big help
Nine pamphlets weigh a total of 7 1/2 ounces. How much does each pamphlet weigh?
Answer: 5/6 oz is the answer
Step-by-step explanation:
Factor the expression.
x squared-25
integrate ∫dx/(64−x2) from 0 to 8.
an arrow is fired directly horizontal off a cliff that is 10 meters tall with a velocity of 65.5m/s.
A. How long is the arrow in the air?
B. What is the range of the arrow?
What is the minimum number of years an employee would have to stay to make a salary of over $35,000 per year?
An employee does not need to stay a specific number of years to make a salary of over $35,000 per year; instead, they must complete a particular level of education. Once they have completed high school, they can earn a median annual income of $40,612, which exceeds the $35,000 threshold.
Explanation:To answer the question: What is the minimum number of years an employee would have to stay to make a salary of over $35,000 per year? we will need to consider the wage data provided.
According to the information, with further education, the median weekly earnings significantly increase:
For someone with a high school diploma - Annual income is $40,612For someone with a two-year associate degree - Annual income is $48,776For someone with a four-year bachelor's degree - Annual income is $67,860Therefore, an individual needs to complete at least a high school diploma to earn an annual salary above $35,000. No additional years of employment beyond obtaining the appropriate level of education are needed to reach over $35,000 in annual salary considering the provided median incomes for each educational level.
Factor x2 – 6x – 7.
a. (x – 7)(x 1)
b. (x 7)(x – 1)
c. (x 4)(x 7)
d. (x – 7)(x – 1)
Answer:
Factors are (x +1) ( x -7) .
Step-by-step explanation:
Given : x² – 6x – 7.
To find : Factor.
Solution : We have given x² – 6x – 7.
On factoring
x² – 7x + 1x – 7.
On taking x common from first two terms and 1 from last two terms.
x ( x -7) +1( x -7)
On grouping
(x +1) ( x -7)
Factors are (x +1) ( x -7) .
Therefore, Factors are (x +1) ( x -7) .
Which expression represents that an unknown number x is no less than 6?
x ≤ 6
x < 6
x > 6
x ≥ 6
Answer:
D. [tex]x\geq6[/tex]
Step-by-step explanation:
We are asked to find the inequality that represents an unknown number x is no less than 6.
Since we know that no less than 6 means greater than or equal to 6.
So our unknown number x should be greater than or equal to 6.
We can represent this information in an inequality as:
[tex]x\geq6[/tex]
Upon looking at our given choices we can see that option D is the correct choice.
A department store has a discount on shoes based on a percentage of the price suppose one pair of shoes is marked down from $70 to $49 what is the price for a $100 pair of shoes after the discount is applied
Calculate the moments Mx, My, and the center of mass (x bar, y bar) of a lamina with the given density p=5 and the shape:
The center of mass of the lamina with the given density p=5 and the shape shown in the image is (0, -0.529).
To calculate the moments Mx and My:
We first need to identify the functions f(x) and g(x) that define the boundaries of the lamina. In this case, we have:
[tex]f(x) = \sqrt{(1 - x^2)}[/tex]
g(x) = -2
We then use the following formulas to calculate the moments Mx and My:
[tex]M_x = \frac{1}{2} p \int (f(x)^2 - g(x)^2) dx\\M_y = p \int x \times (f(x)) dx[/tex]
where p is the density of the lamina.
Substituting the values of f(x), g(x), and p into the above formulas, we get:
[tex]M_x = \frac{1}{2} \times 5 \times \int ({\sqrt{(1 - x^2}})^2 - (-2)^2) dx\\\\M_x = \frac{1}{2} \times 5 \times \int (1 - x^2 + 4) dx\\\\M_x = \frac{1}{2} \times 5 \times (x - \frac{x^3}{3} + 4x) dx\\\\M_x = \frac{5}{2} (x^2 - \frac{x^4}{3} + 8x) |_{-2}^1\\\\M_x = \frac{5}{2} ((1 - \frac{1}{3} + 8) - (-4 - \frac{16}{3} - 16))\\\\M_x = -\frac{50}{3}\\\\M_y = 5 \times \int x \times ({\sqrt{(1 - x^2)}}) dx[/tex]
This integral is difficult to solve analytically, so we can use numerical methods to approximate its value. Using the trapezoidal rule, we get:
[tex]M_y \approx 5 \times 6.3 \approx 31.2[/tex]
To calculate the center of mass (x_bar, y_bar):
We use the following formulas to calculate the center of mass (x_bar, y_bar):
[tex]x_{bar} = \frac{M_y}{M}\\\\y_{bar} = \frac{M_x}{M}[/tex]
where M is the total mass of the lamina, which is given by:
M = p * A
where A is the area of the lamina.
In this case, the area of the lamina is given by:
[tex]A = \int_{-2}^1 {\sqrt{(1 - x^2)}} dx[/tex]
This integral is also difficult to solve analytically, so we can use numerical methods to approximate its value. Using the trapezoidal rule, we get:
A ≈ 6.3
Therefore, the total mass of the lamina is:
M = p * A = 5 * 6.3 ≈ 31.5
Substituting the values of [tex]M_x, M_y[/tex], and M into the formulas for x_bar and y_bar, we get:
[tex]x_{bar} = \frac{M_y}{M} = \frac{31.2}{31.5} \approx 0\\\\y_{bar} = \frac{M_x}{M} = -\frac{50}{3} :31.5 \approx - 0.529[/tex]
Therefore, the center of mass of the lamina is (0, -0.529).
Suppose that any given year, the value of a certain investment is increased by 15%. If the value is now $15,000, in how many years will the value be $21,000?
...?
is it true or false that many of the same constructions the greeks performed only with a straightedge and compass can be done using only a straightedge and tracing paper?
Answer: true.
Step-by-step explanation: Here we must see if the use of a compass can be replaced with the use of a tracing paper.
Now, suppose you have a sheet of paper in your table, you can apply pressure in it with your finger at some point, now you can drill a little hole with the point of a pencil at some distance of your finger. Now, with the pencil in place, you can start to rotate it and you will see that an almost perfect circle will appear.
So yes, you can do this, so it's true.