The Nichols family consists of 8 children and 2 adults. The family minivan can safely transport a total of 7 family members, including an adult driver.
Which number line illustrates the capacity of the Nichols minivan as an inequality?
Answers
x: number of people who will use the family minivan.
We have then:
"The family minivan can safely transport a total of 7 family members, including an adult driver":
x <= 7
Answer:
x <= 7
A number line that illustrates the capacity of the Nichols minivan as an inequality is:
option C)
Related Questions
Please help me out here.
Answers
When you multiply two exponents with the same base together, you can add the indexes together. For example, if you had y * y², you could make it y³, by adding the indexes of 2 and 1.
In this scenario, you can look at the last choice, where it has [tex] x^{9} [/tex] * x. You add the indexes of 9 and 1, to get [tex] \sqrt[3]{ x^{10} } [/tex]
That's equivalent to the equation given, so your answer would be the last choice.
Solve 6,394 divided by 42 =
Answers
The required quotient is [tex]152[/tex] and remainder is [tex]10[/tex].
Given that [tex]6394[/tex] ÷ [tex]42[/tex].
Long division states that [tex]divident= divisor*quotient+remainder[/tex].
Let [tex]a[/tex] and [tex]b[/tex] be any real number. Consider [tex]a[/tex] ÷ [tex]b[/tex] gives
[tex]a=bq+r[/tex], [tex]q[/tex] is quotient [tex]r[/tex] is remainder and its value is [tex]0\leq r < b[/tex].
[tex]\begin{array}{ccccc}42)&006394(152&\\-&42____________&\\&219& \\&\\-&210&\\&0094\\-&0084\\&0010\end{array}\right][/tex]
Hence, the required quotient is [tex]152[/tex] and remainder is [tex]10[/tex].
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______________ is process that you can do over and over, where each result does not affect the next.
Ex. Flipping a coin, rolling dice, choosing a card, etc.
Answers
Which compound inequality can be used to solve the inequality |3x+2|>7
Answers
Answer:
x>[tex]\frac{5}{3}[/tex].
Step-by-step explanation:
We have given an inequality |3x+2|>7.
We need to solve this inequality |3x+2|>7, and find the compound which can solve this.
We know that, inequality :
|3x+2|>7
Subtrating 2 from both sides,
|3x+2-2|>7-2
3x>5
Dividing by 3 both sides,
[tex]\frac{3x}{3} > \frac{5}{3}[/tex]
x>[tex]\frac{5}{3}[/tex]
Therefore, we can see that on the inequality |3x+2|>7, we find x>[tex]\frac{5}{3}[/tex] compound.
Answer:
D. 3x + 2 < –7 or 3x + 2 > 7
Step-by-step explanation:
Aaron solved an inequality and then graphed the solution as shown below. Anwser: A
A student found the solution below for the given inequality lx-9l less than 4
Anwser: D
Amber is solving the inequality lx+6l - 12 less than 13 by graphing. Which equations should Amber graph?
Anwser: A
What is the solution, if any, to the inequality l3xl greater than or equal to 0?
Anwser: A
Which compound inequality is equivalent to lax-bl greater than c for all real numbers a, b, and c, where c is greater than or equal to 0?
Anwser: D
Which compound inequality is equivalent to the absolute value inequality lbl greater than 6?
Anwser: D
What is another way to write the absolute value inequality lpl less than or equal to 12?
Anwser: A
What is the solution to the inequality lx-4l less than 3?
Anwser: B
Which inequality is equivalent to lx-4l less than 9?
Anwser: B
Hope This Helps!
A campground owner plans to enclose a rectangular field adjacent to a river. the owner wants the field to contain 180,000 square meters. no fencing is required along the river. what dimensions will use the least amount of fencing?
Answers
The area is the product between the two sizes:
[tex]A=xy[/tex] (1)
While the perimeter is twice the sum of the two sizes:
[tex]p=2(x+y)[/tex] (2)
From (1) we can write
[tex]y= \frac{A}{x} [/tex]
and we can substitute it into (2):
[tex]p=2(x+ \frac{A}{x})=2x+2 \frac{A}{x} [/tex]
To find the minimum value of the perimeter, we have to calculate its derivative and put it equal to zero:
[tex]p'(x)=0[/tex]
The derivative of the perimeter is
[tex]p'(x) = 2 -2 \frac{A}{x^2}= \frac{2x^2-2A}{x^2} [/tex]
If we require p'(x)=0, we find
[tex]x^2=A[/tex]
[tex]x= \sqrt{A} = \sqrt{180000 m^2}=424.26 m [/tex]
And the other side is
[tex]y= \frac{A}{x}= \frac{180000 m^2}{424.26 m} =424.26 m[/tex]
This means that the dimensions that require the minimum amoutn of fencing are (424.26 m, 424.26 m), so it corresponds to a square field.
The depth of a lake, dd, varies directly with rr, the amount of rainfall last month. if kk is the constant of variation, which equation represents the situation?
Answers
let d be the depth and r be the rainfall amount
dαr
thus
d=kr
where, k is the constant of proportionality, thus the formula will be:
d=kr
An artist is creating a large conical sculpture for a park. The cone has a height of 16 m of and a diameter of 25 m. Find the volume the sculpture to the nearest hundredth.
A. 833.33 m3
B. 7,850 m3
C. 2,616.67 m3
D. 209.33 m3
Answers
The volume of the conical sculpture is calculated using the formula for the volume of a cone, 1/3πr²h. Substituting the given values, the volume is found to be approximately 2,616.67 m³.
Explanation:The subject of this question is focused on calculating the volume of a cone. To find the volume of a cone, we apply the formula 1/3πr²h, where r is the radius and h is the height. Given in the question, the height (h) of the cone is 16 m and the diameter is 25 m. The radius is half of the diameter so it is 25/2 = 12.5 m. Substituting these values into the formula gives us:
Volume = 1/3πr²h
= 1/3 * π *(12.5 m)² * 16 m
≈ 2,616.67 m³
So, the volume of the sculpture to the nearest hundredth is approximately 2,616.67 m³. Thus, Option C is the correct answer.
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Using a straightedge, or using technology, sketch an obtuse, scalene triangle. Make sure to include your sketch in your answer.
Answers
A sphere has a diameter of 12 ft. What is the volume of the sphere? Give the exact value in terms of pi
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Radius = 12 ÷ 2 = 6 ft
[tex]\text {Volume = } \dfrac{4}{3} \pi r^3[/tex]
[tex]\text {Volume = } \dfrac{4}{3} \pi (6)^3 = 288 \pi \text{ ft}^3[/tex]
your answer is here..
given the diameter of the sphere is 12 ft.
therefore radius of the sphere = 12/2 = 6 ft
[tex]volume \: of \: the \: sphere = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \pi( {6}^{3} ) \\ \\ = \frac{4}{3} \pi(216) \\ \\ = 288\pi {ft}^{3} \\ \\ cheers...[/tex]
How do you know the sum of a positive and negative integer will be negative?
Answers
[tex]8+(-3)=+5[/tex]
If what you're asking is, under what condition will the sum of a positive and negative be negative, then it's when the absolute value of the negative number is greater than the positive number. For example:
positive number: 8
negative number: -10
[tex]8+(-10)=-2[/tex]
This sum is negative. Note that [tex]\mid{-10}\mid\ \textgreater \ 8[/tex].
ivan began to prove the law of sines using the diagram and equations below. sin(A) = h/b, so b sin(A) = h. sin(B) = h/a, so a sin(B) = h. Therefore, b sin(A) = a sin(B). Which equation is equivalent to the equation b sin(A) = a sin(B)?
edit: the answer is b!
Answers
(B.) sin(A)/a = sin(B)/b
Kelly wants to know if the number of words on a page in her geometry book is generally more than the number of words on a page in her science book. She takes a random sample of 25 pages in each book, then calculates the mean, median, and mean absolute deviation for the 25 samples of each book.
Kelly claims that because the mean number of words on each page in the science book is greater than the mean number of words on each page in the geometry book, the science book has more words per page. Based on the data, is this a valid inference?
Answers
Answer:
No, because there is a lot of variability in the science book data
Step-by-step explanation:
A system of equations that has an infinite number of solutions is called a(n) ______ system of equations.
Answers
A system of equations with an infinite number of solutions is known as a consistent and dependent system. These systems occur when equations are essentially the same, leading to all solutions satisfying all the equations, often represented by overlapping graphs in the case of linear equations.
Explanation:A system of equations that has an infinite number of solutions is called a consistent and dependent system of equations. When a system is consistent and dependent, it means that the equations describe the same line or geometric shape, leading to an infinite number of points that satisfy all equations in the system simultaneously. This scenario often arises when the equations in the system are multiple forms of the same equation, or when they can be algebraically manipulated to become the same equation.
In practical terms, if you were to graph the equations in a consistent and dependent system, you would see that they overlap completely. For instance, if two linear equations represent the same line, any point on that line is a solution to both equations, hence the infinite solutions. A key aspect of understanding such systems is realizing that they do not lead to a single unique solution but rather a set of solutions that satisfy all conditions outlined by the equations in the system.
A system of equations with an infinite number of solutions is referred to as a consistent and dependent system, indicating the equations describe the same line.
A system of equations that has an infinite number of solutions is called a consistent and dependent system of equations. This type of system occurs when the equations involved describe the same geometric line, meaning every point on the line is a solution to the system, hence an infinite number of solutions. Such systems often arise in various mathematical contexts, including linear algebra and differential equations, where they indicate a fundamental underlying symmetry or redundancy in the system's constraints.This occurs when the equations are dependent, leading to multiple possible solutions that satisfy all the equations simultaneously.
20 POINTS!
Verify the identity.
Answers
[tex]R_s=\left(\dfrac{1}{\sin x}-1\right):\dfrac{\cos x}{\sin x}=\left(\dfrac{1}{\sin x}-\dfrac{\sin x}{\sin x}\right)\cdot\dfrac{\sin x}{\cos x}\\\\=\dfrac{1-\sin x}{\sin x}\cdot\dfrac{\sin x}{\cos x}=\dfrac{1-\sin x}{\cos x}\cdot\dfrac{1+\sin x}{1+\sin x}=\dfrac{1-\sin^2x}{\cos x(1+\sin x)}\\\\=\dfrac{\cos^2x}{\cos x(1+\sin x)}=\dfrac{\cos x}{1+\sin x} \\\\L_s=R_s[/tex]
[tex]Used:\\\csc x=\dfrac{1}{\sin x}\\\\\cot x=\dfrac{\cos x}{\sin x}\\\\\sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\(a-b)(a+b)=a^2-b^2[/tex]
A basketball player has a 50 chance of making each free throw. what is the probability that the player makes at least eleven out of twele free throws
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Select the property that allows the statement 10 = y to be written y = 10.
Commutative - addition
Distributive
Associative - multiplication
Symmetric
Commutative - multiplication
Associative - addition
Identity - addition
Answers
This is the symmetric property
Hope this helps!
The property that allows the statement 10 = y to be written y = 10 is:
Symmetric
Step-by-step explanation:We know that for any set A. if a and b are two elements of the set A.
Then if a is related to b by some relation then by the symmetric property b must be related to a by the same property.
Here 10 is related to y by the equality relation.
i.e. 10=y
Hence, by the symmetric property we have that y must be related to 10 by the same equality relation.
i.e. y=10
Two cities are 45 miles apart. Two trains, with speeds of 70 mph and 60 mph, leave the two cities at the same time so that one is catching up to the other. How long after the trains leave will they be 10 miles apart for the first time? How long after the trains leave will they be 10 miles apart for the second time?
Answers
The first time the two trains are 10 miles apart is approximately 16.15 minutes after they start. The second time they are 10 miles apart is about 25.38 minutes after they start.
Explanation:This problem is a relative speed problem in mathematics, specifically in the subsection of algebra known as rate, time, and distance problems. To solve, you should consider that when the two trains move towards each other, their speeds add up. Hence, the relative speed of the two trains is 70 mph + 60 mph = 130 mph.
First, we need to figure out the time it would take for the trains to be 10 miles apart for the first time. This would be when they have collectively traveled 35 miles (45 miles initial separation - 10 miles final separation). To find the time it takes, we use the formula d=rt, where d is distance, r is rate or speed, and t is time. Here, time t = d/r = 35 miles / 130 mph = approximately 0.27 hours, which converts to about 16.15 minutes.
Next, to find the time when they are 10 miles apart for the second time, we need to consider when they have covered the total distance of 45 miles and then kept going until they've covered an additional 10 miles. This is a total of 55 miles. Again, using the time formula t = d/r, we get t = 55 miles / 130 mph = approximately 0.42 hours or about 25.38 minutes.
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a glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. if a single marble is chosen at random from the jar, what is the probability that it is red
Answers
[tex] \frac{1}{10} [/tex]
What is the value of c when the expression 21.2x + c is equivalent to 5.3(4x − 2.6)?
Answers
To find our answer we need to work out the parenthesis. This is for instance possible using rainbow technique.
[tex]5.3(4x - 2.6) = \\ 5.3 \times 4x - 5.3 \times 2.6 = \\ 21.2x - 13.78[/tex]
Therefore the value of c = - 13.78.
~ Hope this helps you!
Comparing with 21.2x + c:-
the value of c = -13.78 Answer
use formulas to find the lateral and surface are of the given prism the numbers are 5.39m 26m 5m 2m
Answers
Total Surface Area:
(add to the above)
2(1/2)(3)(2) = 6m^2 (area of the two triangles)
6 + 149 = 155m^2
Item 18 A spherical ball with a volume of 972π in.3 is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the ball. What is the volume of the box?
Answers
Volume of the given box is 5832 in³
Volume of the cube:
Given a spherical ball with a volume of 972π in.³,
Since the volume of a sphere is (4/3)πr³, we can find that the radius of the sphere is 9 inches.
The edge length of the cube (box) is twice the radius (diameter of the sphere), so the edge length of the cube is equal to 18 inches.
The volume of the cube is then (18³) in³
Volume of the cube = 5832 in³
if 3x+2y=12 and -4x+6y=24 what is the value of -x+2y
Answers
(2) -4x+6y=24
Solving the system of equations using the method of substitution:
Isolating y in the first equation:
(1) 3x+2y=12→3x+2y-3x=12-3x→2y=12-3x→2y/2=(12-3x)/2→y=(12-3x)/2
Replacing "y" by (12-3x)/2 in the second equation:
(2) -4x+6y=24
y=(12-3x)/2→-4x+6[(12-3x)/2]=24
Solving for x:
-4x+3(12-3x)=24
-4x+36-9x=24
-13x+36=24
-13x+36-36=24-36
-13x=-12
-13x/(-13)=-12/(-13)
x=12/13
Replacing "x" by 12/13 in y=(12-3x)/2
x=12/13→y=[12-3(12/13)]/2
y=(12-36/13)/2
y={[(13)(12)-36]/13}/2
y=[(156-36)/13]/2
y=(120/13)/2
y=(120/13)(1/2)
y=60/13
x=12/13; y=60/13
-x+2y=-12/13+2(60/13)
-x+2y=-12/13+120/13
-x+2y=(-12+120)/13
-x+2y=108/13
Answer: The value of -x+2y is 108/13
Divide £770 in the ratio of 4:3 plsss
Answers
[tex]\bf 4:3\qquad \cfrac{4}{3}\qquad \cfrac{4\cdot \frac{770}{4+3}}{3\cdot \frac{770}{4+3}}\implies \cfrac{4\cdot 110}{3\cdot 110}\implies \cfrac{440}{330}[/tex]
The problem is in the first picture and the questions are in the second one. I have no idea how to do any of this.
Answers
You are given that CB = 271 feet. You are also given that <CAB = 30 degrees.
So you can use Sin(<CAB) = opposite / hypotenuse or
hypotenuse = opposite / sin(<CAB)
hypotenuse = 271 / 0.5
hypotenuse (AB) = 542 feet.
Problem B
CD = 772 feet Given in table
<ACD = 74o Given on drawing.
We need to find AC which is not given
Cos 30 = adjacent / hypotenuse.
adjacent = hypotenuse * Cos(30)
adjacent = AB * Cos(30)
Adjacent = 542 * cos(30)
Adjacent = AC = 469.4 feet
Now we need to start again
AC = 469.4
<ACD = 74
CD = 772
AD = ???
AD^2 = AC^2 + CD^2 - 2 * AC * CD * Cos(74)
AD^2 = 595984 + 220336.4 - 399538
AD^2 = 416782.1
AD = sqrt(416782.1)
AD = 645.59
Problem 3
I'll set it up for you. And give you the answer I get, but I'm going to leave it to you mostly. It just follows what I've done above.
DC = 645.59
CE = 561
DE = 543
DC^2 = CE^2 + DE^2 - 2* CE * DE * Cos(E)
645.59^2 = 561^2 + 543^2 - 2*561*543 * Cos(E)
Cos(E) = -0.3164
E = cos-1(0.3164)
E = 108.45 degrees.
You roll a number cube and flip a coin. find the probability of rolling an even number and flipping heads. write your answer as a fraction in simplest form.
Answers
Hope this helped!
Final answer:
To calculate the combined probability of rolling an even number on a number cube and flipping heads on a coin, you multiply the separate probabilities of each event, which are 1/2 and 1/2 respectively, resulting in a combined probability of 1/4.
Explanation:
The probability of rolling an even number on a number cube (which is a standard six-sided die) is 3 out of 6 since there are three even numbers (2, 4, 6) and six possible outcomes overall. This simplifies to 1/2. The probability of flipping heads on a coin is 1/2 since there are two possible outcomes, heads or tails, and both are equally likely if the coin is fair.
To find the combined probability of two independent events (rolling an even number and flipping heads), you multiply the probabilities of each event together. So, the probability of rolling an even number and flipping heads is 1/2 (for the number cube) times 1/2 (for the coin), which equals 1/4 or 25%.
In the simplest form, the fraction is written as 1/4.
How to solve this problem
Answers
Solve for y
Cos(A) = adjacent / hypotenuse
Cos(A) = y / 8
y = 8 * cos(A)
y = 8 * cos(73)
y = 8 * 0.2924
y = 2.339
Step Two
Solve for x
Sin(A) = opposite / hypotenuse
Sin(73) = x / 8
x = 8 * sin(73)
x = 8 * 0.9563
x = 7.550
Check
x^2 + y^2 =? 8^2
2.339^2 + 7.55^2 =? 8^2
5.471 + 58.53 =? 64
64.000921 = 64 which is close enough.
Find the equation of the line.
A) y= -3/2 x + 1
B) y= -2/3 x - 1
C) y= 2/3 x + 1
D) y= 3/2 x - 1
Answers
Hope this helps
Answer:
It’s y=2/3x+1 that’s the equation of the line.
Step-by-step explanation:
Find the base area of a rectangular pyramid whose pyramid height is 5 cm and slant height of one side of the base is 13 cm and another side of the base is 7 cm.
a. 92√6 cm^2
b. 96√6 cm^2
c. 180√6 cm^2
d. 100√6 cm^2
e. 198√6 cm^2
Answers
x------> the larger side of the rectangular base
y-------> the smaller side of the rectangular base
we know that
Applying the Pythagoras theorem
for the larger side of the base
slant height =13 cm
h=5 cm
13²=5²+(x/2)²-----> (x/2)²=13²-5²-----> 144
(x/2)²=144------> x/2=12------> x=24 cm
for the smaller side of the base
slant height =7 cm
h=5 cm
7²=5²+(y/2)²-----> (y/2)²=7²-5²-----> 24
(y/2)²=24------> y/2=√24------> y=4√6 cm
the area of the base is
24*4√6------> 96√6 cm²
the answer is the option
b. 96√6 cm^2
Graph the six terms of a finite series where a1 = −3 and r = 1.5.
Answers
For the given series:
[tex]a_{1}=-3 \\ r=1.5 [/tex]
Each term of the geometric series is obtained by multiplying the previous term by common ratio.
So the next terms will be:
-4.5, -6.75, -10.125, -15.1875, -22.78125
The general formula for the G.P would be:
[tex] a_{n}=-3(1.5)^{n-1} [/tex]
On plotting the series, the result will be like this:
Answer:
the answer is C
Step-by-step explanation:
There are 100 students in a drawing contest, and 58 of them are girls. What percent of the students in the contest are girls?
Answers
There are 100 students in a drawing contest and 58 of students are girls. What percent of students in the drawing contest are girls?
The fraction [tex]\frac{58}{100}[/tex] represents the number of girls in the drawing contest out of all the students.
To find out what percent of the students are in the drawing contest, we can change [tex]\frac{58}{100}[/tex] into a percent.
We can first reduce the fraction by dividing both the numerator and denominator by the Greatest Common Factor of 58 and 100 using 2.
58 ÷ 2 = 29
100 ÷ 2 = 50
Our reduced fraction is [tex]\frac{29}{50}[/tex].
29 ÷ 50 = 0.58
0.58 × 100 = 58%
Therefore, 58% of the students in the drawing contest are girls.