Which ordered pairs are solutions to the inequality y−4x≥−5 ?
Select each correct answer.
(−2, 1)
(−4, 2)
(4, 0)
(5, −2)
(1, −1)
Answer:
The correct answers are
(-2,1)
(-4,2)
(1,-1)
Step-by-step explanation:
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Find the volume of a sphere with a diameter 40 cm in length. Approximate pi as 3.14 and round your answer to the nearest tenth.
-20,480 , -5,120 , -1280 , -320 what goes next
Emma uses 5 ounces of milk to make a shake.she want to buy enough milk to make 7 shake and she want to buy the smallest size container ok milk that she can.should she buy a pint a quart or gallon of milk?justify your answer Help
the sum of three consecutive integers if the last integer is z.
a.) 3z+3
b.) 3z+6
c.)3z-3
d.)3z
The sum of three consecutive integers where the last integer is z is 3z - 3.
Explanation:The sum of three consecutive integers can be derived using the concept of arithmetic series. For instance, if z represents the last of the three consecutive integers, we know that the numerals preceding it are z-1 and z-2. Hence, the sum of these three integers would be (z-2) + (z-1) + z.
Simplifying this, we get 3z - 3 which corresponds to option c.)3z-3 in the question's list.
Remember, an important aspect of sequences and series is that the numbers are arranged in a specific order.
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Jane has a 5 × 7-inch photograph that she wants enlarged to a 10 × 14-inch photograph.
What is the scale factor from the original photograph to the enlarged photograph?
compare the 5 and 10 dimension then the 7 and 14 dimensions
10/5 =2
14/7 =2
they both are the same ratio/factor
the factor is 2
Answer:
2:1
Step-by-step explanation:
it asks for the scale since 5 x 2 = 10 and 7 x 2 = 14
the scale is 2 : 1
6 tractors take 10 days to collect the harvest. How long would it take 15 tractors to do the same amount of work
Scott puts some sports stickers in rows. He makes 6 rows with 5 stickers in each row. If he puts the same number of stickers in 5 equal rows, how many stickers would be in each row?
Answer:
6 stickers.
Step-by-step explanation:
We have been given that Scott makes 6 rows with 5 stickers in each row.
The total number of stickers in 6 rows would be:
[tex]\text{The total number of stickers}=6\times 5[/tex]
[tex]\text{The total number of stickers}=30[/tex]
Therefore, there are 30 stickers in 6 rows.
We need to find the number of stickers in 5 rows having the same number of stickers.
Since there are 30 stickers in total, so the number of stickers in each row would be 30 stickers by 5 rows.
[tex]\text{The number of stickers in each row}=\frac{30}{5}[/tex]
[tex]\text{The number of stickers in each row}=6[/tex]
Therefore, there would be 6 stickers in each row.
x3-27i=0 solve for the root equation
Stu is laying brick down to make a patio. He plans for the patio to be 12.5 feet by 18.3 feet. He orders enough brick for 247 square feet. Which statement about the amount of brick is correct?
Answer:
Stu estimated correctly by rounding up.
He ordered enough brick.
The exact area is [tex]228.75[/tex] square feet
Step-by-step explanation:
we know that
the area of the patio is equal to
[tex]A=bh[/tex]
In this problem we have
[tex]b=12.5\ ft, h=18.3\ ft[/tex]
substitute in the formula
[tex]A=12.5*18.3=228.75\ ft^{2}[/tex]
[tex]228.75\ ft^{2}< 247\ ft^{2}[/tex]
Sam opened a savings account with an initial deposit of $2,000. Since then, he has never made any other deposits or withdrawals. His savings account earns 0.4% interest monthly and an annual bonus of 1.5% interest. Which equation gives the approximate amount, A(x), he has in his savings account as a function of x, the number of years since his initial deposit?
A(x) ≈ 2,000 + (1.059)x3
A(x) ≈ 2,000(1.019)x2
A(x) ≈ 2,000(1.065)x
A(x) ≈ 2,000(1.059)x2
Answer:
Third option:
[tex]A(x)\approx 2,000(1.065)^x[/tex]
Step-by-step explanation:
Notice if we invest 2,000 then the first month then after the first 0.4% interest is earned we will have in the account:
2,000(1+0.004) = 2,000(1.004)
I just applied the simple interest formula.
Then after the second month we will have:
[tex]2,000(1.004)(1.004) = 2,000(1.004)^2[/tex]
And so on each month.
So at the end of the first year (12 months) we have:
[tex]2,000(1.004)^{12}[/tex]
But we also earn an additional 1.5% in the year, so we will have:
[tex]2,000(1.004)^{12}(1.015)[/tex]
At the end of the second year we will have:
[tex]2,000[(1.004)^{12}(1.015)]^2[/tex]
At the end of the third year:
[tex]2,000[(1.004)^{12}(1.015)]^2[/tex]
And so on,
So if the number of years is denoted with x, at the end of x years we will have the following amount in the savings:
[tex]2,000[(1.004)^{12}(1.015)]^x[/tex]
We use our calculator to simplify that inside the brackets:
[tex](1.004)^{12}(1.015)=1.06481[/tex]
Rounding to the third decimal place we get: 1.065
So notice the amount in the savings after x years will be:
[tex]2,000(1.065)^x[/tex]
Since they want it in function notation we just write the A(x) that denotes the amount in the savings:
[tex]A(x)\approx 2,000(1.065)^x[/tex]
Which of the following statements must be true about a rectangle? Choose all answers that apply: Choose all answers that apply: A It has four sides of equal length. B It has four right angles. C It has two pairs of parallel opposite sides.
Answer:
The correct answers are options B and C.
Step-by-step explanation:
B It has four right angles.
C It has two pairs of parallel opposite sides.
All angles are right angles by definition of a rectangle. The rectangle has 2 pairs of parallel opposite sides.
Option A is wrong as its a square whose all 4 sides have equal length.
Find the work done by the force field f(x, y, z) = y + z, x + z, x + y on a particle that moves along the line segment from (1, 0, 0) to (5, 3, 2).
Final Answer:
Word done = 31 units
Explanation:
To find the work done by a force field [tex]$\mathbf{F}(x, y, z)$[/tex] on a particle moving along a path, we can use the line integral of the force field along that path.
First, we need to define the force field [tex]$\mathbf{F}(x, y, z)$[/tex] and the parametric equations for the line segment.
Given the force field
[tex]$$\mathbf{F}(x, y, z) = \langle y + z, x + z, x + y \rangle,$$[/tex]
we have the following components:
[tex]F_x &= y + z, \\\\F_y &= x + z, \\\\F_z &= x + y.[/tex]
Now, let's find the parametrization of the line segment from the point (1,0,0) to the point (5,3,2). We can define a vector [tex]$\mathbf{r}(t)$[/tex] that describes this line segment by
[tex]$$\mathbf{r}(t) = \mathbf{r_0} + t(\mathbf{r_1} - \mathbf{r_0}),$$[/tex]
where [tex]$\mathbf{r_0} = \langle 1, 0, 0 \rangle$[/tex] is the starting point, [tex]$\mathbf{r_1} = \langle 5, 3, 2 \rangle$[/tex] is the ending point, and t is a parameter that goes from 0 to 1.
So we have
[tex]\mathbf{r}(t) &= \langle 1, 0, 0 \rangle + t(\langle 5, 3, 2 \rangle - \langle 1, 0, 0 \rangle) \\\\ &= \langle 1, 0, 0 \rangle + t\langle 4, 3, 2 \rangle \\\\ &= \langle 1 + 4t, 3t, 2t \rangle.[/tex]
From the parametric equation, we have the components:
[tex]x(t) &= 1 + 4t, \\\\y(t) &= 3t, \\\\z(t) &= 2t.[/tex]
The line integral of the force field along the path can be computed by
[tex]$$W = \int_C \mathbf{F} \cdot d\mathbf{r},$$[/tex]
where [tex]$d\mathbf{r}$[/tex] is the differential element along the path C, and the dot product represents the scalar product of the force field and the differential path element.
We can express [tex]$d\mathbf{r}$[/tex] in terms of t as
[tex]$$d\mathbf{r} = \mathbf{r}'(t) dt = \langle \frac{dx}{dt}, \frac{dy}{dt}, \frac{dz}{dt} \rangle dt = \langle 4, 3, 2 \rangle dt.$$[/tex]
Then the work done is
[tex]W &= \int_{t=0}^{t=1} \mathbf{F}(x(t), y(t), z(t)) \cdot \mathbf{r}'(t) dt \\\\ &= \int_{0}^{1} \langle 3t + 2t, 1 + 4t + 2t, 1 + 4t + 3t \rangle \cdot \langle 4, 3, 2 \rangle dt \\\\ &= \int_{0}^{1} [(5t)(4) + (6t + 1)(3) + (7t + 1)(2)] dt \\\\ &= \int_{0}^{1} [20t + 18t + 3 + 14t + 2] dt \\\\ &= \int_{0}^{1} [52t + 5] dt \\\\ &= [26t^2 + 5t]_{0}^{1} \\\\ &= 26(1)^2 + 5(1) - (26(0)^2 + 5(0)) \\\\ &= 26 + 5 \\\\ &= 31.[/tex]
So, the work done by the force field [tex]$\mathbf{F}(x, y, z)$[/tex] on the particle as it moves along the line segment from (1, 0, 0) to (5, 3, 2) is 31 units of work.
What are 2 ways three people can share fifths?
Final answer:
Three people can share fifths by dividing one pie into five slices and each taking three, or dividing three pies into fifteen slices and each person getting one slice from each pie. Both methods ensure each person receives three-fifths of a pie.
Explanation:
Two ways that three people can share fifths involve division and allocation of pie (or any other divisible whole). One way is to take a single pie, divide it into five equal slices, and each person takes three slices. However, since we need to divide these among three people and a pie has only five slices, we'll end up with a fraction of a slice per person. The second way is to start with three pies, divide them so that there are a total of fifteen slices (five slices per pie), and then each person gets one slice from each pie, totaling three slices per person.
Here are two arithmetic representations of the scenarios:
First method: (3 slices/person) / 5 slices = 3/5 per personSecond method: 1 slice from each of 3 pies / 5 slices per pie = 3/5 per personWhether we are dealing with one pie or three, each person ends up with the same fraction of the total available pie: three-fifths.
what is the sum of (1-5q)+2(2.5q+8)
Answer:
17
Step-by-step explanation:
Eliminating parentheses, we have ...
... 1 - 5q +2·2.5q +2·8
... = 1 -5q +5q +16 . . . . . carry out the multiplication
... = q(-5+5) +(1 +16) . . . . group like terms
... = q·0 +17 . . . . . . . . . . . combine like terms
... = 17
Daniel dives into a swimming pool. The height of his head is represented by the function h(t) = -8t(squared) - 28t + 60, where t is the time in seconds and h(t) is the height of his head, in inches. How many seconds will it take for Daniel's head to reach the surface of the pool?
A person made an estimate for a three–minute interval. the estimate was 241.5 seconds. what was the error of this estimate?
What is the 250th term of this sequence. Please explain. 4, 9,14,19,24
Find the value of c for which the line 3x +cy= 5 is parallel to the y axis,
the line L1 has equation 2x + y = 8. The line L2 passes through the point A ( 7, 4 ) and is perpendicular to L1 . Find the equation of L2.
Answer: [tex]x-2y+7=0[/tex]
Step-by-step explanation:
Given : The line[tex]L_1[/tex] has equation [tex]2x + y = 8[/tex]
In intercept form : [tex]y =-2x+8[/tex]
The slope of [tex]L_1[/tex] =-2 [in intercept form equation of line [tex]y =mx+c[/tex], m is slope ]
Let p be slope of [tex]L_2[/tex]
We know that when two lines are perpendicular then the product of their slopes is -1.
[tex]\Rightarrow\ -2\times p=-1\\\\\Rightarrow\ p=\dfrac{1}{2}[/tex]
The equation of line having slope 'm' and passing through (a,b) is given by :-
[tex](y-b)=m(x-a)[/tex]
Then , equation of line [tex]L_2[/tex] will be :-
[tex](y-7)=\dfrac{1}{2}(x-7)\\\\\Rightarrow\ 2y-14=x-7\\\\\Rightarrow\ x-2y+7[/tex]
You and your frend step into identical row-boats. you notice that your boat sinks into the water twice as far as your friends. what can you say about your friend's weight compared with yours? your friend weighs twice as much as you your friend weighs the same as you your friend weighs half as much as you your friend weighs one fourth your weight
Delta airlines quotes a flight time of 2 hours, 5 minutes for its flights from cincinnati to tampa. suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.what is the probability that the flight will be no more than 5 minutes late (to 2 decimals)?
The likelihood that the flight will be no more than 5 minutes late would be equal to a flight that arrives between 2 hours and 2 hours and 10 minutes.
So the answer would be:
P (5 late or less) = 10 * 1/20 = 0.5
The answer is 0.5
But if we are looking for the probability of the flight that would be 10 minutes late, the likelihood of that event would be 0.25.
Final answer:
The probability that a Delta airlines flight from Cincinnati to Tampa will be no more than 5 minutes late, given that the actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes, is 0.50.
Explanation:
The question deals with the uniform distribution of flight times and calculating the probability that a flight will be no more than 5 minutes late. Assuming flight times are uniformly distributed between 2 hours (120 minutes) and 2 hours, 20 minutes (140 minutes), the total range of flight times is 20 minutes (140 minutes - 120 minutes).
Delta airlines quotes a flight time of 2 hours, 5 minutes, which is 125 minutes. Therefore, a flight being no more than 5 minutes late means the flight time would be at most 130 minutes. To find the probability that the flight time is 130 minutes or less, we calculate the proportion of the distribution that falls within this range.
The probability that the flight will be no more than 5 minutes late is the length of the interval from 120 minutes to 130 minutes divided by the total range (20 minutes), which is (130 - 120) / 20 = 10 / 20 = 0.5. Thus, the probability is 0.50 to two decimal places.
One canned juice drink is 25% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 15L that is 17% orange juice
Find the point on the plane 2x+5y+z=8 that is nearest to (2,0,1).
Answer:
(2.2, 0.5, 1.1)
Step-by-step explanation:
The parametric equation of the line normal to the plane and through point (2, 0, 1) can be written ...
... L = (2, 0, 1) + t(2, 5, 1)
We want to find the value of t (and the corresponding point) that makes L satisfy the equation of the plane.
... 2(2+2t) +5(0 +5t) +1(1+t) = 8 . . . . . put values from L in for x, y, z in plane
... 5 + 30t = 8 . . . . . simplify
... t = (8 -5)/30 = 0.1 . . . . solve for t (subtract 5, divide by 30)
For this value of t, L is ...
... (2, 0, 1) + 0.1(2, 5, 1) = (2.2, 0.5, 1.1)
If total liabilities are $200,000 and total assets are $325,000, owner's equity would be: 2)
a. $525,000
b. $200,000
c. $125,000
d. impossible to determine from the given data
Julianna works 32 hours each week. She earns $14.15 an hour. Which is closest to the amount of money Julianna will earn if she works for 46 weeks.(Please show work?)
A) $16,800
B) $18,000
C) $21,000
D) $22,500
Julianna will earn $22,579.20 if she works for 46 weeks, which is closest to the option D) $22,500.
Explanation:To calculate the amount of money Julianna will earn if she works for 46 weeks, we need to multiply the number of work hours per week (32) by the hourly wage ($14.15), and then multiply that result by the number of weeks worked (46). This can be calculated as follows:
Total earnings = (32 hours/week) × ($14.15/hour) × (46 weeks)
Total earnings = $22,579.20
Therefore, the closest amount of money Julianna will earn if she works for 46 weeks is $22,579.20, which is closest to option D) $22,500.
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. Hot dogs come in packs of 8. Hot dog rolls come in packs of 12. What is the least number of packs of each Shawn should buy to have enough to serve 24 people and have none left over?
What is the volume of a sugar cube that measure 1cm on each side? what is the cross-sectional area of the cube? the total surface area?
Billy wants to live in the area defined by y < 3x − 6. Explain how you can identify the houses in which Billy is interested in living. (2 points)
A line has a slope of between the points (10,5) and (16,n).
What is the value of n?
8
2
10
16
6