To determine how many cars in the lot are red, we need to find one-third of the total number of cars. In this case, we are told that one out of every three cars is red, so the probability of a randomly chosen car being red is 1/3. The calculation is: Number of red cars = 54 * (1/3) = 18 cars.
Explanation:To determine how many cars in the lot are red, we need to find one-third of the total number of cars. In this case, we are told that one out of every three cars is red, so the probability of a randomly chosen car being red is 1/3.
To calculate how many cars out of 54 are red, we can multiply the total number of cars by the probability of a car being red:
Number of red cars = 54 * (1/3) = 18 cars
Therefore, there are 18 cars that are red in the lot.
what is the equation of this circle in general form
Suppose your friends parents invest $15,000 in an account paying 4% annually. What will the balance be after 9 years?
Fahim is 6 feet tall. At noon, he stands with the sun behind him casting a shadow. The distance from the top of Fahim’s head to the furthest tip of the shadow is 13 feet. [Not drawn to scale] What is the length of Fahim’s shadow? Round to the nearest tenth of a foot.
7.0 feet
8.5 feet
11.5 feet
14.3 feet
Answer: 11.5 feet
Step-by-step explanation:
Given: The height of Fatim = 6 feet
At noon, he stands with the sun behind him casting a shadow. Also, Fatima is standing vertical to the ground such that a right triangle is formed.
Let the length of Fahim’s shadow be x.
By Pythagoras theorem , we have
[tex]13^2=x^2+6^2\\\\\Rightarrow169=x^2+36\\\\\Rightarrow\ x^2=169-36\\\\\Rightarrow\ x^2=133\\\\\Rightarrow x=\sqrt{133}=11.5325625947\approx11.5[/tex]
Hence, the length of Fahim’s shadow =11.5 feet
1. One box of cereal is 16 ounces and costs $3. A smaller box of The same cereal is 11.5 ounces and costs $2. Which box of cereal is the better but? Explain.
2. I'm an N-guage model train set, a tank car is 3.75 inches long. The actual tank car is 50 feet long. What is the ratio of the length of the actual tank car to the length of the model tank car?
3. 9 km/1 hour = ?m/ 1 second
What is the solution to this system of equations?
2/3x + y = 6
-2/3x - y = 2
A. (1, -1)
B. (0, 8)
C. infinitely many solutions
D. no solution
When the given system of equations is added together, it simplifies to '0=8', which is a contradiction. Therefore, the system of equations has no solution.
Explanation:You can simply add the two equations together. Adding the two equations eliminates the variables x and y:
(2/3x - 2/3x) + (y - y) = 6 + 2
This simplifies to 0 = 8, which is a contradiction. Therefore, this system of equations has no solution. That means the correct answer is D. 'No solution'.
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Use Euler’s Formula to find the missing number ?
Faces:21
Vertices:14
Edges:?
A.34 B.32 C.33 D.36
What is the depth and volume of this rectangular prism in cubes and cubic inches?
-8r - 2 + 7r= -9
solve the equation. then check the solution
A car listens plate is made up of 7letters or numbers, where the numbers are whole numbers 0-9.
Suppose the license plate is randomly generated, one character at a time.
What is the probability the first character is a number?
Enter you sender as a decimal rounded to the nearest hundredth
Is 3.2 meters equal to 320 millimeters?
Please need some help on this
27 PTS + BRAINLIEST. I need all of these questions answered. I will award brainliest to the fastest and most correct answer. I will report unrelated answers.
ex: 2a. -4x
how many vertices does a sphere have?
Final answer:
A sphere has no vertices as it is a three-dimensional shape with a continuous curved surface, unlike a cube which has distinct edges and flat faces.
Explanation:
The question "how many vertices does a sphere have?" can be answered quite simply. A sphere is a perfect three-dimensional shape where every point on the surface is equidistant from the center. Unlike a cube, which has flat faces and edges, a sphere has a continuous curved surface. Consequently, a sphere does not have any vertices, edges, or faces. Vertices are points where edges intersect, and since a sphere has no edges or flat faces, it cannot have vertices.
McCune Landscaping buys 100 shovels for $15 each. McCune sells all 100 shovels at $29.99. What is the profit?
find the limit of (sqrt(x+5)-4)/(x-11) as x approaches 11
[tex] \lim\limits_{x\to11}\dfrac{\sqrt{x+5}-4}{x-11}=\lim\limits_{x\to11}\dfrac{(\sqrt{x+5}-4)(\sqrt{x+5}+4)}{(x-11)(\sqrt{x+5}+4)}\\\\=\lim\limits_{x\to11}\dfrac{(\sqrt{x+5})^2-4^2}{(x-11)(\sqrt{x+5}+4)}=\lim\limits_{x\to11}\dfrac{x+5-16}{(x-11)(\sqrt{x+5}+4)}\\\\=\lim\limits_{x\to11}\dfrac{x-11}{(x-11)(\sqrt{x+5}+4)}=\lim\limits_{x\to11}\dfrac{1}{\sqrt{x+5}+4}=\dfrac{1}{\sqrt{11+5}+4}\\\\=\dfrac{1}{\sqrt{16}+4}=\dfrac{1}{4+4}=\dfrac{1}{8}\\\\Answer:\ d.\ \dfrac{1}{8} [/tex]
Sarah has grades of 98 and 98 on her first two tests. If she wants an average of at least 80 after her third test, what score must she make on that test
Sarah must score at least 44 on her third test in order to have an average of at least 80.
Explanation:To find out what score Sarah must make on her third test in order to have an average of at least 80, we can set up an equation. The average of her three test scores can be calculated by adding up her scores and dividing by 3:
Average = (98 + 98 + x) / 3
We want the average to be at least 80, so we can solve the equation for x:
(98 + 98 + x) / 3 ≥ 80
Simplifying the equation, we get:
196 + x ≥ 240
Subtracting 196 from both sides, we have:
x ≥ 44
Therefore, Sarah must score at least 44 on her third test in order to have an average of at least 80.
Sarah needs to score at least a 44 on her third test to have an average of at least 80 across her three test scores.
Explanation:Sarah has grades of 98 and 98 on her first two tests and wants to have an average of at least 80 after her third test. To calculate the minimum score Sarah must make on the third test to achieve her goal, we use the formula for the average of three numbers, which is (test1 + test2 + test3) / 3. In Sarah's case, the average after three tests should be at least 80.
Let's represent the third test score as 'x'. Thus, the equation to find 'x' becomes:
(98 + 98 + x) / 3 ≥ 80
Combining the scores of the first two tests gives us:
(196 + x) / 3 ≥ 80
By multiplying both sides by 3 to eliminate the denominator, we have:
196 + x ≥ 240
Subtract 196 from both sides to solve for x:
x ≥ 240 - 196
x ≥ 44
Therefore, Sarah must score at least a 44 on her third test to achieve an average of 80.
when divided by 3, i am 700. when divided by 7, i am 300. what number am i?
The unknown number is equal to 2100.
How to determine the equation representing the situation?In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:
Let the variable n represent the unknown number.
"when divided by 3, I am 700."
n/3 = 700 ...equation 1.
n = 700(3)
n = 2100.
"when divided by 7, I am 300."
n/7 = 300 ....equation 2.
n = 300(7)
n = 2100.
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On the Algebra test the number of students who got a grade A was three more than twice the number of students who got lower grades. How many A's were there if total number of students in the Algebra class is 24?
Is (4,-2) a solution to the equation 5x - y = 18?
Show your work please!
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Please Help!
which of the following expressions is equivalent to the expression below? 4/7*5/9 a.5/9/ 4/7 b.4/7 /5 /9 c.4/9 / 5/7 d.4/7 /
To simplify the expression 4/7 * 5/9, the equivalent expression is 20/63.
Explanation:To simplify the expression 4/7 * 5/9, we can multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator. So, the expression becomes 20/63. Therefore, none of the options listed are equivalent to 4/7 * 5/9.
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None of the options a, b or c are equivalent to the expression 4/7*5/9. The correct expression must simplify to 20/63.
Explanation:The question is asking to find out which of the provided expressions is equivalent to the expression 4/7*5/9. The correct option should yield the same result as the original expression when calculated. The expression 4/7*5/9 simplifies to 20/63.
Let's check the provided options:
Option a: 5/9 divided by 4/7 simplifies to 35/36, which is not equal to 20/63.Option b: 4/7 divided by 5/9 simplifies to 36/35, which is also not equal to 20/63. Option c: 4/9 divided by 5/7 simplifies to 28/45, which is not equal to 20/63.The provided information about relative frequencies is irrelevant for this question.
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The table shows the data of a random sample of fish that were collected from and later released into a lake.
Type of Fish Bass Eel Gar
Number of Fish 92 56 52
How many bass are estimated to be present if a sample of 1,000 fish is collected from the lake?
1: 184
2: 292
3: 420
4: 460
Match the trinomials with their factors. Tiles a2 + a − 20 a2 − 9a + 20 a2 − 8a − 20 a2 − 12a + 20 a2 − 19a − 20 Pairs Factors Trinomials (a − 4)(a − 5) arrowBoth (a − 10)(a − 2) arrowBoth (a − 4)(a + 5) arrowBoth (a − 10)(a + 2) arrowBoth
Trinomial [tex]a^2 + a - 20[/tex] with factors (a + 5)(a - 4)
Trinomial [tex]a^2 - 9a + 20[/tex] with factors (a - 4)(a - 5)
Trinomial [tex]a^2 - 8a - 20[/tex] with factors (a - 10)(a + 2)
Trinomial [tex]a^2 - 12a + 20[/tex] with factors (a - 10)(a - 2)
To match the trinomials with their factors, we can factor each trinomial and compare the factors given:
1. Factorizing trinomial [tex]a^2 + a - 20:[/tex]
The factors are (a + 5)(a - 4).
This matches with the pair (a - 4)(a + 5).
2. Factorizing trinomial [tex]a^2 - 9a + 20:[/tex]
The factors are (a - 4)(a - 5).
This matches with the pair (a - 4)(a - 5).
3. Factorizing trinomial [tex]a^2 - 8a - 20[/tex]:
The factors are (a - 10)(a + 2).
This matches with the pair (a - 10)(a + 2).
4. Factorizing trinomial [tex]a^2 - 12a + 20:[/tex]
The factors are (a - 10)(a - 2).
This matches with the pair (a - 10)(a - 2).
Therefore, the correct matches are:
- Trinomial [tex]a^2 + a - 20[/tex] with factors (a + 5)(a - 4)
- Trinomial [tex]a^2 - 9a + 20[/tex] with factors (a - 4)(a - 5)
- Trinomial [tex]a^2 - 8a - 20[/tex] with factors (a - 10)(a + 2)
- Trinomial [tex]a^2 - 12a + 20[/tex] with factors (a - 10)(a - 2)
The list shows the scores made be each member of Jaime's discussion group on the last test. 69 79 62 93 73 81 73 78 Which box-and-whiskers plot correctly displays the information? f Box-and-whiskers plot G g Box-and-whiskers plot J h Box-and-whiskers plot F j Box-and-whiskers plot H
Final answer:
To choose the correct box-and-whiskers plot for Jaime's discussion group scores, we must calculate the five key statistics and match them with a plot displaying those exact values, factoring in the majority of scores in the 70-89 range.
Explanation:
To determine which box-and-whiskers plot correctly displays Jaime's discussion group scores, we need to calculate five key statistics: the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and the maximum. These statistics help us create an accurate box plot representation of the dataset.
First, we organize the scores in ascending order: 62, 69, 73, 73, 78, 79, 81, 93. From here, we can identify the minimum (62) and maximum (93) scores directly. The median score will be the average of the fourth and fifth scores since we have an even number of observations, which is (73+73)/2 = 73. The lower quartile (Q1) is the median of the lower half of the data, which would be (69+73)/2 = 71. The upper quartile (Q3) is the median of the upper half of the data, which is (79+81)/2 = 80.
Now that we have all the necessary statistics, we can select the box plot that matches these values. Jaime's scores are mostly within the 70-89 range, reflecting a majority of C and B grades, with a few scores in the 60-69 and 90-100 ranges, which correspond to D/F and A ranges respectively. The correct box-and-whiskers plot will show a box ranging from Q1 (71) to Q3 (80), a median line at 73, a whisker extending to the minimum score of 62, and another whisker extending to the maximum score of 93.
There are 3 black marbles and 4 red marbles in a bag.
What is the probability of picking a black marble, replacing it back in the bag, and then choosing another black marble?
1) 3/8
2) 9/49
3) 5/13
4) 1/7
This morning, a convenience store had 21 granola bars in stock. The store sold 6 granola bars throughout the day. If the store will receive a shipment of 42 granola bars tomorrow, how many granola bars will it have in stock?
After selling 6 out of 21 granola bars, the store has 15 left. Following a shipment of 42 granola bars, the store will have a total of 57 granola bars in stock.
To find out how many granola bars the store will have in stock after the shipment, we should first calculate how many granola bars are left after the sales by subtracting the number sold from the initial stock. They started with 21 granola bars and sold 6, so they have 21 - 6 = 15 granola bars left. Then, we add the number of granola bars in the shipment arriving tomorrow to the number they currently have in stock. They will receive 42 granola bars in the shipment, so the total will be 15 + 42 = 57 granola bars in stock after the shipment arrives.
Is (5,6.5) a solution to y= -1/2x + 9?
Show your work please!!
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Events A and B are mutually exclusive. Also, P(A) = 0.12 and P(B) = 0.25.
What is P(A or B)?
A. 0.13 B. 0.03 C. 0.25 D. 0.37
two joggers run 8 miles north and then 5 miles west. what is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point? round to the nearest tenths place
The shortest distance they travel to return to starting point is 9.43 miles.
Since, two joggers run 8 miles north and then 5 miles west.
According to question , a right triangle is formed. and hypotenuse of right triangle represent the shortest distance between starting point to final point.
Apply Pythagoras theorem,
Shortest distance, [tex]=\sqrt{8^{2}+5^{2} } =\sqrt{64+25}=\sqrt{89}=9.43miles[/tex]
Thus, They travel 9.43 miles to return to their starting point.
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A pop star is coming for a live concert in your area. The ticket proceeds will benefit a nonprofit organization helping underprivileged children interested in music education. They would like to raise $1,500. Stage-level seats are on sale for \$10 each and balcony-level seats are on sale for \$5 each. How many of each seat type would need to be sold to reach the goal of \$1,500?
Please really need help :(
Find the diameter of a sphere with the volume 7776pi in^3
Answer:
The diameter is 36 inches
Step-by-step explanation:
The volume of a sphere is
[tex] \frac{4}{3} \pi {r}^{3} [/tex]
The given sphere has volume
[tex]7776\pi {in}^{3} [/tex]
We can now equate the formula to the given volume and solve for r.
[tex]\frac{4}{3} \pi {r}^{3} = 7776\pi[/tex]
[tex] {r}^{3}= 7776\pi \times \frac{3}{4\pi} [/tex]
[tex] {r}^{3} = 5832[/tex]
[tex]r = \sqrt[3]{5832} [/tex]
[tex]r = 18[/tex]
The diameter of the sphere is twice the radius.
Hence
[tex]diameter = 2 \times 18 = 36in[/tex]