Answer: the correct option is (B) x = 6.
Step-by-step explanation: Given that x varies inversely as v and x = 48 when v = 8.
We are to find the value of x when v = 64.
Since x varies inversely as v, so we have
[tex]x\propto\dfrac{1}{v}\\\\\\\Rightarrow x=k\dfrac{1}{v}~~~~~~~~~~~~~~~~~~[\textup{where k is the constant of proportionality}][/tex]
When x = 48 and v = 8, then, we get
[tex]48=\dfrac{k}{8}\\\\\Rightarrow k=48\times8\\\\\Rightarrow k=384.[/tex]
So,
[tex]x=\dfrac{384}{v}~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Therefore, when v = 64, then from equation (i), we get
[tex]x=\dfrac{384}{64}=6.[/tex]
Thus, the required value of x is 6.
Option (B) is CORRECT.
What are the solutions to the following system?
Answer:
C
Step-by-step explanation:
Jack is building a rectangular fence for his ferret. He has 20 feet of fencing and wants the short side of the fence to be 7/2 feet. How long will the other side of the fence be? Write the answer in decimal form.
General Idea:
When we are working with word problems, we need to follow the below steps:
Step 1: Assign variable for the unknown that we need to find.
Step 2: Write a meaningful mathematical equation using the sentence given
Step 3: Solve the equation by Performing reverse operation by Undoing whatever is done to the variable. Solving means find the value of the variable which will make the equation TRUE.
Applying the concept:
Step 1: Let 'x' be the length of longest side of the fence.
Step 2: We need to set up an equation based on the information given.
[tex] Perimeter\; of\; rectangle=\; 2(\; Longest \; side\; +\; Shortest \; side\; ) [/tex]
Substituting 20 for the perimeter of rectangle, x for Longest side and [tex] \frac{7}{2} [/tex] for the shortest side in the above formula, we get the below equation.
[tex] 2(x+\frac{7}{2} )=20 [/tex]
Step 3: Solving the equation.
[tex] 2(x+\frac{7}{2} )=20\\ Distribute \; 2 \; in \; the \; left \; side \; of \; the \; equation\\ \\ 2x+2 \cdot \frac{7}{2} =20\\ Simplify \; in \; the\; left\; side \; of \;the \;equation\\ \\ 2x+7=20\\ Subtract \; 7 \;on\; both \;sides \; of\; the \; equation\\ \\ 2x+7-7=20-7\\ Combine\; like \; terms\\ \\ 2x=13\\ Divide \; by \; 2\;on \; both\; sides\\ \\ \frac{2x}{2} =\frac{13}{2} \\ Simplify \; fraction\;on \; both \; sides\\ \\ x=6.5 [/tex]
Conclusion:
The length of longest side of the fence is 6.5 feet.
Kala bought two types of cheese at a deli. She bought 0.50 pound of American cheese and 1.25 pounds of Swiss cheese. The bar diagram and equation below represent Kala’s purchase, where p represents the total number of pounds of cheese she bought.
What is the total number of pounds of cheese Kala bought?
0.75
1.20
1.30
1.75
Answer:
The total number of pounds of cheese Kala bought is 1.75 pounds
Step-by-step explanation:
Kala bought two types of cheese at a deli.
She bought 0.50 pound of American cheese and 1.25 pounds of Swiss cheese.
The total number of pounds of cheese Kala bought
= 0.50+1.25
= 1.75 pounds
Hence, the total number of pounds of cheese Kala bought is:
1.75 pounds
5.11 find the probability of a couple having a baby girl when their third child is born, given that the first two children were both girls. assume boys and girls are equally likely. is the result the same as the probability of getting all girls among three children?
Matthew bought 4 new compact discs at $16.99 each and a carrying case for $35.89. He paid 2007-03-04-00-00_files/i0250000.jpg% sales tax on his purchases. If Matthew paid $112.42 total, determine if he paid the correct amount. a. Matthew paid $0.15 too little for his purchases. b. Matthew paid $0.16 too much for his purchases. c. Matthew paid $0.05 too much for his purchases. d. Matthew paid the correct amount for his purchases.
PLEASE HELP
Missi designed a stained glass window and made a scale drawing using centimeters as the unit of measurement. She originally planned for the length of the window to be 44 in. but decided to change it to 48 in. If the length of the window in her scale drawing is 4 cm, which statement about the change of scale is true?
A)One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale.
B)One cm represented 44 in. in the first scale, but now 1 cm represents 48 in. in the second scale.
C)One cm represented 1 in. in the first scale, but now 1 cm represents 1 in. in the second scale.
D)One cm represented 12 in. in the first scale, but now 1 cm represents 11 in. in the second scale.
Answer:
The correct answer is option A,
One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale
Step-by-step explanation:
The earlier planned length was [tex]44 in\\[/tex]
So the scale of the map was
[tex]\frac{44}{4} \\= 11\\1 cm = 11 in\\[/tex]
The second planned length was [tex]48 in\\[/tex]
So the second scale of the map was
[tex]\frac{48}{4} \\= 12\\1 cm = 12 in\\[/tex]
Thus, option A is correct.
the numbers of wins and losses of two local basketball teams are on the table find the probability that a randomly selected game from the season was played by the wolves given that it was a lose
Probability is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability that a randomly selected game from the season was played by the wolves given that it was a loss is 1/5.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Total number of wins and losses = 12 + 14 + 16 + 18 = 60
Number of losses wolves has = 12
Now,
The probability that a randomly selected game from the season was played by the wolves given that it was a loss.
= 12/60
= 1/5
Thus,
The probability that a randomly selected game from the season was played by the wolves given that it was a loss is 1/5.
Learn more about probability here:
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PLEASE explain this, I'm so lost. 25 points! What is the area of the base of the pyramid? Enter your answer in the box. Express your answer in radical form.
The answer is:
area of base = [tex]12\sqrt{3}[/tex]
Hope it helps!
Find the surface area of the rectangular solid.
l=16 in, w=13 in, h=15in.
Surface area is in inches and to the 2nd power.
In oder to join a yoga club there is a $100 annual fee and a $5 fee for each class ytouattend. Write an equation in slope-intercept form that models this situation.
banananana help me i need you
Answer:
Banananana. How do you know that person?
Step-by-step explanation:
3. what is a popular sunday activity for families in mexico city ? ( 1point )
A. vista the beach
b. visit the prado museum
c. stroll by the roman aqueduct
d. go to the chapultepec park
Factor completely 12a3d2 − 6ad3. Prime 6a3d3(2a − d) 6ad2(2ad − d) 6ad2(2a2 − d)
In winter, the price of apples suddenly went up by 0.75 per pound. Sam bought 3 pounds of apples at the new price for a total of $5.88
Using the definitions of odd and even functions , explain why y=sin x+1 is neither odd or even
Final answer:
The function y = sin x + 1 is neither even nor odd because it does not satisfy the conditions f(x) = f(-x) for even functions and f(-x) = -f(x) for odd functions after substitution and simplification.
Explanation:
An even function is defined as a function that satisfies the condition f(x) = f(-x), showing symmetry about the y-axis. An odd function, on the other hand, satisfies the condition f(-x) = -f(x), indicating symmetry about the origin. To determine if y = sin x + 1 is an odd or even function, we must check these conditions.
Applying the even function definition, we would expect sin(-x) + 1 = sin(x) + 1 which is not true because sin(-x) = -sin(x) and thus does not satisfy the required symmetry. When we apply the odd function test, we expect -(sin x + 1) = sin(-x) + 1, which also doesn't hold because -sin(x) - 1 does not equal sin(-x) + 1. Therefore, y = sin x + 1 is neither odd nor even.
Imari went on a hike and recorded the number of each type of bird he saw. The circle graph shows the results of his count. Imari saw 42 sparrows. How many birds did he count in all? Enter your answer in the box. A pie chart depicting a count for bird species. Cardinals are at 13 percent, Sparrows are at 35 percent, Chickadees are at 23 percent, Blue Jays are at 8 percent, Woodpeckers are at 4 percent, and Robins are at 17 percent.Imari went on a hike and recorded the number of each type of bird he saw. The circle graph shows the results of his count. Imari saw 42 sparrows. How many birds did he count in all?
Answer: 120
Hope This Helps ^_^
Which best describes the function on the graph?
Please help me! I don't know the answer.
Lines L and M are parallel. GEOMETRY
The angle measure of ∠2 is equal to 38°.
m∠2 = 38°.
What are the corresponding angles?When two parallel lines are crossed by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).
Given:
Lines L and M are parallel lines.
And the parallel lines are cut by a traversal line.
From the property of corresponding angles:
The angle measure of ∠2 is equal to 38°.
Therefore, m∠2 = 38°.
To learn more about the corresponding angles;
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will give branliest Which events are mutually exclusive?
Jon eats more than 1 apple; Jon eats 3 apples.
Jon eats 4 apples; Jon eats 1 apple.
Jon eats 2 apples; Jon eats more than 2 apples.
Jon eats 2 apples; Jon eats 4 apples.
Answer:
Jon eats 2 apples; Jon eats more than 2 apples.
Step-by-step explanation:
Mutually exclusive events are events which have no common element between them. They are completely disjoint and the intersection would be a null set
Hence probability for the intersection of mutually exclusive events =0
Here we are given 4 options to select.
Jon eats more than 1 apple; Jon eats 3 apples.
These two are not mutually exclusive as eating 3 apples includes eating 1 apple.
Jon eats 4 apples; Jon eats 1 apple.
These two are not mutually exclusive as eating 4 apples includes eating 1 apple.
Jon eats 2 apples; Jon eats more than 2 apples.
These two are mutually exclusive since he cannot eat 2 applies exactly and also more than 2 apples
Jon eats 2 apples; Jon eats 4 apples.
These two are not mutually exclusive as eating 4 apples includes eating 2 apple.
Hence correct answer is
Jon eats 2 apples; Jon eats more than 2 apples.
Dora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 12.
Please someone help me !!! Thank you !!
Which measure describes how all of the values of a data set vary with a single number?
A) mean
B) median
C) mode
D) range
Answer:
The answer is d. range.
What is the equation of the exponential graph shown?
In the United States, the mean average height of adult women is approximately 65.5 inches, with a standard deviation of 2.5 inches. If height is normally distributed,what percent of the women in this country are between 63 and 70.5 inches tall?
The lowest common denominator for the fractions 8/64 and 8/32 is ?
Final answer:
The lowest common denominator for the fractions 8/64 and 8/32 is 32. This is found by identifying 32 as the least common multiple of the denominators 64 and 32, allowing both fractions to be expressed with the same denominator.
Explanation:
Finding the Lowest Common Denominator
To find the lowest common denominator (LCD) for the fractions 8/64 and 8/32, you must identify the smallest number that both denominators can divide into without leaving a remainder. Both 64 and 32 can be divided by 32, so the LCD for these fractions is 32. It's important to understand that finding an LCD involves looking for the least common multiple (LCM) of the denominators. In this case, since 32 is a multiple of 64 (32x2=64), it serves as the LCM of 32 and 64, and consequently, the LCD of the fractions.
To further clarify, each fraction can be expressed with a denominator of 32. For 8/64, when we divide both the numerator and denominator by 8, we get 1/8. This fraction can then be converted to have a denominator of 32 through multiplication by 4 (1/8 * 4/4 = 4/32). Similarly, the fraction 8/32 is already expressed with the desired denominator.
By finding the LCD, it is easier to perform addition, subtraction, or comparison of fractions, as they will share the same denominator.
The lowest common denominator for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( \boxed{64} \).[/tex]
To find the lowest common denominator (LCD) for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \)[/tex], we need to determine the least common multiple (LCM) of the denominators 64 and 32.
Step 1: Find the prime factorization of each denominator:
[tex]- \( 64 = 2^6 \)[/tex]
[tex]- \( 32 = 2^5 \)[/tex]
Step 2: Determine the LCM by taking the highest power of each prime that appears in any factorization:
[tex]\[ \text{LCM} = 2^{\max(6, 5)} = 2^6 = 64 \][/tex]
Therefore, the LCD of the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( 64 \).[/tex]
Step 3: Verify that ( 64 ) is indeed the LCD:
[tex]- \( \frac{8}{64} = \frac{1}{8} \)[/tex]
[tex]- \( \frac{8}{32} = \frac{1}{4} \)[/tex]
Both fractions can be rewritten with a denominator of ( 64 ):
[tex]- \( \frac{1}{8} = \frac{8}{64} \)[/tex]
[tex]- \( \frac{1}{4} = \frac{16}{64} \)[/tex]
Therefore, ( 64 ) is the lowest common denominator for[tex]\( \frac{8}{64} \) and \( \frac{8}{32} \).[/tex]
Thus, the lowest common denominator for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( \boxed{64} \).[/tex]
The ratio of the amount of money Jason has to the amount of money Wilson has is 12:13. After Wilson spent $63, Jason had 3 times as much money as Wilson.
a. How much money did I Jason have?
b. How much money did they have altogether?
what is the vertex of f(x)=5^2+20-16
Ramon earns $1,770 each month and pays $53.70 on electricity. To the nearest tenth of a percent, what percent of Ramon's earnings are spent on electricity each month?
The area of a room is 396 square feet. The length is x+3, and the width is x+7 feet. Find the dimensions of the room
Which postulate or theorem can be used to prove that △JKL is similar to △MKN?
A. SSS Similarity Theorem
B. ASA Similarity Theorem
C. AA Similarity Postulate
D. SAS Similarity Theorem
Answer:
The correct option is D.
Step-by-step explanation:
In triangle △JKL,
[tex]\frac{JK}{KL}=\frac{30}{50}=\frac{3}{5}[/tex]
In triangle △MKN,
[tex]\frac{MK}{KN}=\frac{15}{25}=\frac{3}{5}[/tex]
In triangle △JKL and △MKN
[tex]\frac{JK}{KL}=\frac{MK}{KN}[/tex]
[tex]\angle JKL=\angle MKN[/tex] (Vertically opposite angles)
Since two sides are proportional and an inclined angle is congruent, so by SAS theorem of similarity we get
[tex]\triangle JKL=\triangle MKN[/tex]
Therefore option D is correct.