Heather can type the fastest. Comparing the two rates, we can see that Heather's rate of 68 words per minute is higher than Carrie's rate of 65.5833 words per minute.
To determine who can type the fastest, we need to calculate the typing rate in words per minute for both Carrie and Heather.
First, let's calculate Carrie's typing rate:
Carrie can type 787 words in 12 minutes. To find out how many words she can type per minute, we divide the number of words by the number of minutes.
[tex]\[ \text{Carrie's rate} = \frac{787 \text{ words}}{12 \text{ minutes}} \] \[ \text{Carrie's rate} = 65.5833 \text{ words per minute} \][/tex]
Next, let's calculate Heather's typing rate:
Heather can type 1020 words in 15 minutes. Similarly, we divide the number of words by the number of minutes to find her rate.
[tex]\[ \text{Heather's rate} = \frac{1020 \text{ words}}{15 \text{ minutes}} \] \[ \text{Heather's rate} = 68 \text{ words per minute} \][/tex]
Therefore, Heather can type the fastest.
One-Half cup of black provides 15% of the potassium you need daily. You must get the remaining 2890 milligrams from other sources. How many milligrams of potassium should you consume daily?
A conjecture and a portion of the flowchart proof used to prove the conjecture are shown.
Which equation best represents the information that should be in the box labeled 1?
3x = 9
3x = 26
3x = 27
3x = 30
Answer:
The correct option is 3.
Step-by-step explanation:
Given: [tex]\overline {PQ}\cong \overline{QR}[/tex], [tex]PQ=3x-1,QR=26[/tex].
Prove: [tex]x=9[/tex]
[tex]\overline {PQ}\cong \overline{QR}[/tex] (Given)
[tex]PQ=QR[/tex] (Segment congruent postulate)
[tex]3x-1=26[/tex] (Substitution property of equality)
Add 1 on both sides.
[tex]3x-1+1=26+1[/tex] (Addition property of equality)
[tex]3x=27[/tex]
Divide both sides by 3.
[tex]x=9[/tex] (Division property of equality)
Hence proved.
The required equation for box 1 is 3x=27.
Therefore the correct option is 3.
there are 16 sixth graders and 20 seventh graders in a club. the club wants to organize members into equal size groups. each group will only have sixth or only seventh graders.
how many students will be in each group if each group has the greatest number if club members
Solve x2+4x+1=0. Please someone help me
Answer:
x=2+square root 3
Step-by-step explanation:
hope it helps
Determine the slope between the points (-3, 0) and (0, 5)
What is $117 in a ratio of 1:8
Write the number in expanded notation 4,408,730
The place value chart can help us to write a number in expanded notation. When we put 4,408,730 into the place value chart, we can recognize that our number is equal to
4 millions + 4 hundred thousands + 0 ten thousands + 8 thousands + 7 hundreds + 3 tens + 0 units
Image is provided.
Factor the polynomial 4x4 – 20x2 – 3x2 + 15 by grouping. What is the resulting expression? (4x2 + 3)(x2 – 5) (4x2 – 3)(x2 – 5) (4x2 – 5)(x2 + 3) (4x2 + 5)(x2 – 3)
Answer:
Hi there! The answer is to this question is
B. (4x2 – 3)(x2 – 5)
Hope this helps :D
The factored form of the polynomial 4x⁴ – 20x² – 3x² + 15 is (4x² – 3)(x² – 5). The correct option is B.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given polynomial is 4x⁴ – 20x² – 3x² + 15. The polynomial by grouping can be solved as below:-
P = 4x⁴ – 20x² – 3x² + 15
P = 4x² ( x² - 5) -3 ( x² - 5 )
P = (4x² – 3)(x² – 5)
Hence, the factored form of the polynomial 4x⁴ – 20x² – 3x² + 15 is (4x² – 3)(x² – 5).
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The sum of two consecutive integers is 150. what are the two integers ?
The numbers are 74.5 and 75.5
What is algebra?Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values. Here in algebra, these values are often represented with symbols such as x, y, z, p, or q, and these symbols are called variables. Further, these symbols are manipulated through various arithmetic operations of addition, subtraction, multiplication, and division, with an objective to find the values.
Given number:
150
let the consecutive number be x and x+1
Now, according to the question
x+x+ 1= 150
2x + 1 = 150
2x= 149
x= 149/2
x= 74.5
hence, the numbers are 74.5 and 75.5
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Write an equation in point-slope form for the line through the given point with the given slope Point: (3, -4) Slope = 6
Answer: y + 4 = 6(x - 3)
Step-by-step explanation:
The point-slope formula is y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]) where m is the slope and ( [tex]x_1[/tex], [tex]y_1[/tex]) is a point on the graph.
Using the formula given above, we will plug in what we know to write our equation.
y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])
y - (-4) = (6)(x - (3))
y + 4 = 6(x - 3)
Morgan has $60 to spend on clothes. He wants to buy a pair of jeans for $25 and spend the rest on t-shirts. Each t-shirt costs $5. Which inequality represents the number of t-shirts he can purchase? x ≥ 7 x ≤ 16 x ≤ 7 x ≥ 16
Answer:
x ≤ 7
Step-by-step explanation:
What is the area of Figure ABCD?
a) 54 square inches
b) 60 square inches
c) 66 square inches
d) 72 square inches
The largest butterfly in the world is found in Papua,New Guinea.The female butterfly of the species weighs about 9/10 ounce.Use a decimal to write the female's weight.
Chris needs a graphing calculator for math class. He finds a $60 model on sale for 15% off. If he decides to buy this calculator, how much will the sale price be?
48 inches long and 24 inches wide. What is the area of the poster in square feet?
the area of the poster in square feet is, 8 feet²
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Length of poster = 48 inch
Width of poster = 24 inch
Since, We know that;
1 feet = 1 / 12 inch
Hence, Length of poster = 48 / 12
= 4 feet
And, Width = 24 / 12
= 2 feet
Thus, Area of poster = Length x Width
= 4 x 2
= 8 feet²
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the larger of two numbers is nine less than four times the smaller number. If the sum od the two numbers is 76, find both numbers
Answer:
17 and 59
Step-by-step explanation:
Let's find the answer by assuming the following:
L=larger number
S=smaller number
The first condition is: 'L' is nine less than four times 'S' but, because:
(four times 'S') is the same as 4*S then:
('L' is nine less than four times 'S') is equal to ('L' is nine less than 4*S), which means:
L+9=4*S (eq. 1)
Second condition is: the sum of the two numbers is 76, so:
L+S=76 which can be written as:
S=76-L using this relation in eq. 1 we have:
L+9=4*S
L+9=4*(76-L)
L+9=304-4L
L+4L=304-9
5L=295
L=295/5
L=59
And also we have:
L+S=76
S=76-L
S=76-59
S=17
In conclusion, the two numbers are 17 and 59.
evaluate this exponential expression 7*(6+2)^2-3^2
How much will you save if you buy an item listed at $75.50 at a 25% discount?
Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is C(x) = 3050 + 8x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing sells the cleats at $150 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit? Revenue = 150x Correct: Your answer is correct. Profit = 150x−(3050+8x+0.1x2) Correct: Your answer is correct. At least Incorrect: Your answer is incorrect. pairs
To find the profit maximizing quantity, we must calculate and compare total revenue, marginal revenue, total cost, and marginal cost for each unit level, and graph the total revenue, total cost, marginal revenue, and marginal cost curves. The profit maximizing quantity is where marginal revenue equals marginal cost.
Explanation:To determine the profit maximizing quantity, we need to calculate total revenue, marginal revenue, total cost, and marginal cost for each output level of the winter coats sold by Doggies Paradise Inc. Since the firm is perfectly competitive and dog coats sell for $72 each, the marginal revenue is equal to the price, thus $72 for each additional unit sold.
Let's calculate these values and summarize them in a table:
Total Revenue (TR) = Price (P) imes Quantity (Q) = $72 imes QMarginal Revenue (MR) = Change in TR / Change in Q = $72 (constant for each unit since P is constant)Total Cost (TC) = Fixed Costs (FC) + Variable Costs (VC)Marginal Cost (MC) = Change in TC / Change in QThe marginal cost can be found by taking the difference in total variable costs for each additional unit produced plus the fixed costs. It's important to compare MR and MC for each output to find the profit maximizing quantity, where MR=MC. Graphing these will illustrate the intersection point that denotes the optimal output level. The total revenue and total cost curves can also help visualize the point at which profit is maximized, as this is where the distance between the TR and TC curves is largest.
The area of a square garden is one sixteenth
1.
16 squared 2. How long is each side?
In 12 hours, how many more kilometers could the yellow car go than the red car if the red car has an average speed of 217/km per hour and the yellow car has 242 km per hour?
Classify each pair of numbered angles.
Drag and drop the descriptions into the boxes to correctly classify each pair of numbered angles. Each description may be used more than once.
Adjacent
Linear Pair
Vertical
None
The paired numbered angles can be classified as follows:
<5 and <6 are vertical angles
<1 and <2 are none (not vertical, not adjacent, not a linear pair)
Recall the following:
Adjacent angles share a corner and a common side, but do not overlap.Linear pairs are two angles that are adjacent to each other along a straight line.Vertical angles share a common vertex but are not adjacent to each other.Therefore, from the above stated facts, we can conclude that:
<5 and <6 are vertical angles
<1 and <2 are none (not vertical, not adjacent, not a linear pair)
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What is 0.61 repeating as a fraction and how did you get the answer
Answer:
the answer is 61/99
Step-by-step explanation:
melissa is making clothes for her dolls.She has 7/8 yard of fabric.Each doll shirt requires 2/7 of a yard of fabric.How many shirts can she make for her dolls?
Which phrase correctly describes the following expression?(5+23)
The expression (5+23) is correctly described as a simple addition, resulting in a sum of 28. It exemplifies the basic operation of adding two numbers together, an essential mathematical skill.
Explanation:The phrase that correctly describes the following expression (5+23) is simple addition. This expression simply requires adding the two numbers within the parentheses, leading to an answer of 28. Unlike complex expressions that involve multiple operations and rules such as the distributive property or the order of operations (parentheses, exponents, multiplication and division, and addition and subtraction), this expression only requires basic addition.
The concept of addition is fundamental in mathematics, allowing for the combining of two or more numbers to find their total. Such operations are building blocks for more complex arithmetic and algebraic tasks.
It's also important to note that the order in which numbers are added does not change the sum, a principle known as the commutative property of addition.
There are 4680 gym members in total. 3 8 are aged 25 - 59 years, 2 5 are over 60 years and the remainder are under 25 years. How many members are under 25 years?
pi over 7 = a over 4. a=?
The equivalent value of the expression π / 7 = a/4 is a = ( 4π/7 )
Given data:
To find the value of a when given π/7 = a/4, cross-multiplication is done and a is solved as:
When two fractions are equal, to eliminate the denominators, the cross multiplication is executed and the unknown variable is solved.
Cross-multiplying the equation:
π * 4 = 7 * a
Simplifying the equation:
4π = 7a
To solve for a, divide both sides of the equation by 7:
a = (4π) / 7
Hence, the solution of a = ( 4π/7 )
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what property was used to rewrite the polynomial expression
(x+5)+3(a+(6x)y) to (5+x)+3(a+(6x)y)
Zach has 3/4 hour to play video games. it takes him 1/12 hour to set uo the system. Each round of his favorite game takes 1/6 hour. How many rounds can he play
Final answer:
After setting up the system, Zach has 2/3 hour left to play. Since each round takes 1/6 hour, he can play 4 full rounds of his favorite game.
Explanation:
Zach has 3/4 hour to play video games, and it takes him 1/12 hour to set up the system. Each round of his favorite game takes 1/6 hour. To find out how many rounds he can play, we need to subtract the setup time from the total available time and then divide by the time each game takes.
Subtract the setup time from the total time: 3/4 hour - 1/12 hour.Calculate the common denominator and subtract: 9/12 hour - 1/12 hour = 8/12 hour, which simplifies to 2/3 hour.Divide the remaining time by the time per round: 2/3 hour ÷ 1/6 hour.Calculate the number of rounds: 2/3 hour × 6/1 hour = 4 rounds.Zach can play 4 full rounds of his favorite game.
the average adult horse needs 2/5 bale of hay each day to me dietary recommends. Oh horse farm has 44 bales of hay. How many horses can be found in one day with 44 bales of hay?