Answer:
384 cars
Step-by-step explanation:
To find the total number of spaces in the carpark, we must multiply the number of rows by how many cars they can accommodate:
34 ⋅ 40 = 1360
As you can see, we have 1360 total spaces. Since there are 976 cars parked, and we want to find out how many spaces are left, we have to subtract the amount of cars parked from the total spaces.
1360 - 976 = 384
Therefore, our answer is 384, specifically, 384 cars.
Answer:
384 cars.
Step-by-step explanation:
40 * 34 - 976
= 1360 - 976
= 384.
(x + y, 2) = (13, 2x - y)
Answer: (x, y) = (5,8)
Step-by-step explanation:
x + y = 13 2x - y = 2
y = -x + 13
2x - (-x + 13) = 2 3x =15
x=5
x=5 y = -x + 13
y = -(5) + 13 = 8
The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows: y = 2 + 4x What does the y-intercept of this function represent? (1 point) The original height of the plant was 4 mm. The original height of the plant was 2 mm. The height of the plant increases by 2 mm for every hour of sunlight it receives. The height of the plant increases by 4 mm for every hour of sunlight it receives.
Answer:
The original height of the plant was 2 mm
Step-by-step explanation:
Given
[tex]y = 2 + 4x[/tex]
Required
Interpret the y-intercept
The y-intercept is when [tex]x = 0[/tex]
So, we have:
[tex]y = 2 + 4 *0[/tex]
[tex]y = 2 + 0[/tex]
[tex]y = 2[/tex]
This implies that the original or initial height was 2 mm
Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west at 18 mi/h. At what rate (in mi/h) is the distance between the cars increasing two hours later
Answer:
The rate at which the distance between the two cars is increasing is 30 mi/h
Step-by-step explanation:
Given;
speed of the first car, v₁ = 24 mi/h
speed of the second car, v₂ = 18 mi/h
Two hours later, the position of the cars is calculated as;
position of the first car, d₁ = 24 mi/h x 2 h = 48 mi
position of the second car, d₂ = 18 mi/h x 2 h = 36 mi
The displacement of the two car is calculated as;
displacement, d² = 48² + 36²
d² = 3600
d = √3600
d = 60 mi
The rate at which this displacement is changing = (60 mi) / (2h)
= 30 mi/h
1. You are given the 3rd and 5th term of an arithmetic sequence. Describe in words how to determine the general term.
2. You are given the 3rd and 5th term of an geometric sequence. Describe how to determine the 10th term without finding the general term.
Step-by-step explanation:
1. In an arithmetic sequence, the general term can be written as
xₙ = y + d(a-1), where xₐ represents the ath term, y is the first value, and d is the common difference.
Given the third term and the fifth term, and knowing that the difference between each term is d, we can say that the 4th term is x₃+d and the fifth term is the fourth term plus d, or (x₃+d)+d =
x₃+2d. =x₅ Given x₃ and x₅, we can subtract x₃ from both sides to get
x₅-x₃ = 2d
divide by 2 to isolate d
(x₅-x₃)/2 = d
This lets us solve for d. Given d, we can say that
x₃ = y+d(2)
subtract 2*d from both sides to isolate the y
x₃ -2*d = y
Therefore, because we know x₃ and d at this point, we can solve for y, letting us plug y and d into our original equation of
xₙ = y + d(a-1)
2.
Given the third and fifth term, with a common ratio of r, we can say that the fourth term is x₃ * r. Then, the fifth term is
x₃* r * r
= x₃*r² = x₅
divide both sides by x₃ to isolate the r²
x₅/x₃ = r²
square root both sides
√(x₅/x₃) = ±r
One thing that is important to note is that we don't know whether r is positive or negative. For example, if x₃ = 4 and x₅ = 16, regardless of whether r is equal to 2 or -2, 4*r² = 16. I will be assuming that r is positive for this question.
Given the common ratio, we can find x₆ as x₅ * r, x₇ as x₅*r², and all the way up to x₁₀ = x₅*r⁵. We don't know the general term, but can still find the tenth term of the sequence
I need help answering this ASAP
Answer:
A
Step-by-step explanation:
The graph is a square root function
sin(180+0).cos(180+0)/cos(180+0).sin(180-0)
Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives less than 159 miles in a day. Round your answer to four decimal places.
Answer:
the probability that a truck drives less than 159 miles in a day = 0.9374
Step-by-step explanation:
Given;
mean of the truck's speed, (m) = 120 miles per day
standard deviation, d = 23 miles per day
If the mileage per day is normally distributed, we use the following conceptual method to determine the probability of less than 159 miles per day;
1 standard deviation above the mean = m + d, = 120 + 23 = 143
2 standard deviation above the mean = m + 2d, = 120 + 46 = 166
159 is below 2 standard deviation above the mean but greater than 1 standard deviation above the mean.
For normal districution, 1 standard deviation above the mean = 84 percentile
Also, 2 standard deviation above the mean = 98 percentile
143 --------> 84%
159 ---------> x
166 --------- 98%
[tex]\frac{159-143}{166-143} = \frac{x-84}{98-84} \\\\\frac{16}{23} = \frac{x-84}{14} \\\\23(x-84) = 224\\\\x-84 = 9.7391\\\\x = 93.7391\ \%[/tex]
Therefore, the probability that a truck drives less than 159 miles in a day = 0.9374
PLEASE HELP ASAP!!!!!
Step-by-step explanation:
Area ABC=1/2ab×sin C
=1/2 ×20×10 ×Sin C
Sin C =100
a coin is tossed succesively three times times . determine tje probabiliy of getting all three heads
Answer:
Answer : 1/8.
Step-by-step explanation:
Hey there!
Please see the attached picture for your answer.
Hope it helps!
Please send only answer
Want to bring a metal rod to assemble a toy frame. All long metal rods must be used at least. How much to assemble the frame as shown in the picture
Answer:
how many times should u use the metal rod ??
What is the distance between the points (7, 8) and (-8, 0) on a coordinate grid?
Answer:
17 units
Step-by-step explanation:
Use the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Plug in the points and simplify:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]d = \sqrt{(-8 - 7)^2 + (0-8)^2}[/tex]
[tex]d = \sqrt{(-15)^2 + (-8)^2}[/tex]
[tex]d = \sqrt{225 + 64[/tex]
[tex]d = \sqrt{289[/tex]
[tex]d = 17[/tex]
So, the distance between the points is 17 units
Calculate the break even sales dollars if the fixed expenses are $7,000 and the contribution ratio is 40%.
Answer:
Break even sales = $17,500 (Approx.)
Step-by-step explanation:
Given:
Fixed expenses = $7,000
Contribution ratio = 40%
Find:
Break even sales dollars
Computation:
Break even sales = Fixed expenses / Contribution ratio
Break even sales = 7,000 / 40%
Break even sales = 7,000 / 0.40
Break even sales = 17,500
Break even sales = $17,500 (Approx.)
What is the value of x in the equation 5(3x + 4) = 23?
Answer:
x = 1/5
Step-by-step explanation:
5(3x + 4) = 23
Distribute
15x+20 = 23
Subtract 20 from each side
15x+20-20 = 23-20
15x = 3
Divide by 15
15x/15 = 3/15
x = 1/5
Answer:
[tex]x = 0.2[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex]5(3x + 4) = 23[/tex]
[tex](5 * 3x) + (5 * 4) = 23[/tex]
[tex](15x) + 20 = 23[/tex]
Step 2: Subtract 20 from both sides
[tex](15x) + 20 - 20 = 23 - 20[/tex]
[tex]15x = 3[/tex]
Step 3: Divide both sides by 15
[tex]\frac{15x}{15} = \frac{3}{15}[/tex]
[tex]x = \frac{1}{5}[/tex]
[tex]x = 0.2[/tex]
Answer: [tex]x = 0.2[/tex]
a jet flew 2660 miles in 4.75 hours. what is the rate of speed in miles per hour? (the proportion would be 2660:4.75::x:1 set the proportion in fractional form and proceed to find x.)
Set the proportion as shown:
2660/4.75 = x/1
Cross multiply:
4.75x = 2660
Divide both sides by 4.75
x = 560
Answer: 560 miles per hour
Which of the following questions are equivalent to the answer below x 3/5
Answer:
[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex]
[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex]
[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex]
Step-by-step explanation:
Given
[tex]x^\frac{3}{5}[/tex]
Required
The equivalent expressions
We have:
[tex]x^\frac{3}{5}[/tex]
Expand the exponent
[tex]x^\frac{3}{5} = x^{ 3 * \frac{1}{5}}[/tex]
So, we have:
[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex] ----- this is equivalent
Express 1/5 as roots (law of indices)
[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex] ------ this is equivalent
The above can be rewritten as:
[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex] ------ this is equivalent
Please help I need the answer ASAP!!
The hypotenuse will always be the longest side of the triangle. Option C is correct: AB > DC.
AB is the hypotenuse of triangle ABC. Therefore, it is greater than leg AC. AC is the hypotenuse of triangle ACD. If AC is less than AB, then DC must also be less than AB because DC is less than AC.
Hope this helps!
Use the integral test to determine whether the series is convergent or divergent. [infinity] n = 2 n2 n3 + 1 Evaluate the following integral. [infinity] 2 x2 x3 + 1 dx
I think the given series is
[tex]\displaystyle\sum_{n=2}^\infty \frac{n^2}{n^3+1}[/tex]
You can use the integral test because the summand is clearly positive and decreasing. Then
[tex]\displaystyle\sum_{n=2}^\infty\frac{n^2}{n^3+1} > \int_2^\infty\frac{x^2}{x^3+1}\,\mathrm dx[/tex]
Substitute u = x ³ + 1 and du = 3x ² dx, so the integral becomes
[tex]\displaystyle \int_2^\infty\frac{x^2}{x^3+1}\,\mathrm dx = \frac13\int_9^\infty\frac{\mathrm du}u = \frac13\ln(u)\bigg|_{u=9}^{u\to\infty}[/tex]
As u approaches infinity, we have ln(u) also approaching infinity (whereas 1/3 ln(9) is finite), so the integral and hence the sum diverges.
find the equation of straight line passes through point (3,1) such that the intercept on y-axis exceeds that on the x- axis by 4.
Answer:
Step-by-step explanation:
18. A triangle has side lengths of 6, 8, and 9. What type of triangle is it?
•
acute
•
obtuse
•
equiangular
•
right
Answer:
obtuse
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9514 1404 393
Answer:
x = 14 cm
Step-by-step explanation:
We can only solve for x if the triangles are similar. The arrows on the left and right legs say those are parallel. Since alternate interior angles at each of the transversals are congruent, the triangles are AA similar.
ΔABC ~ ΔDEC, so we have ...
EC/ED = BC/BA
x/(18 cm) = (35 cm)/(45 cm)
x = (18 cm)(7/9) = 14 cm
find the two intersection points
(x+1)^2 +(y+2)^2 = 16
3x+ 4y = 1
Show your steps please
Answer:
Our two intersection points are:
[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]
Step-by-step explanation:
We want to find where the two graphs given by the equations:
[tex]\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1[/tex]
Intersect.
When they intersect, their x- and y-values are equivalent. So, we can solve one equation for y and substitute it into the other and solve for x.
Since the linear equation is easier to solve, solve it for y:
[tex]\displaystyle y = -\frac{3}{4} x + \frac{1}{4}[/tex]
Substitute this into the first equation:
[tex]\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16[/tex]
Simplify:
[tex]\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16[/tex]
Square. We can use the perfect square trinomial pattern:
[tex]\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16[/tex]
Multiply both sides by 16:
[tex](16x^2+32x+16)+(9x^2-54x+81) = 256[/tex]
Combine like terms:
[tex]25x^2+-22x+97=256[/tex]
Isolate the equation:
[tex]\displaystyle 25x^2 - 22x -159=0[/tex]
We can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 25, b = -22, and c = -159. Substitute:
[tex]\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}[/tex]
Hence, our two solutions are:
[tex]\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}[/tex]
We have our two x-coordinates.
To find the y-coordinates, we can simply substitute it into the linear equation and evaluate. Thus:
[tex]\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2[/tex]
And:
[tex]\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}[/tex]
Thus, our two intersection points are:
[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]
Help me please and thank you
Answer:
D) 0.89
Step-by-step explanation:
round 0.885 to 0.89
Two chords in a circle intersect. One chord is made of 6 and 5, and the other is made of x +1 and x. What is x?
Answer:
x = 5 and -6
Step-by-step explanation:
Using the intersecting chord theorem which states that the products of the lengths of the line segments on each chord are equal.
Hence:
let
a = 6, b = 5, c = x+1 and d = x
Therefore, ab = cd
6*5 = x(x+1)
30 = x²+x
x²+x - 30 = 0
x²+ 6x - 5x - 30 = 0
x(x+6) - 5(x+6) =0
(x-5)(x+6) = 0
x-5 =0 and x+6 = 0
x = 5 and -6
find the missing side length below brainly
Let it be x
[tex]\\ \sf\longmapsto \dfrac{3}{5}=\dfrac{x}{x+4}[/tex]
[tex]\\ \sf\longmapsto 3(x+4)=5x[/tex]
[tex]\\ \sf\longmapsto 3x+12=5x[/tex]
[tex]\\ \sf\longmapsto 5x-3x=12[/tex]
[tex]\\ \sf\longmapsto 2x=12[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{12}{2}[/tex]
[tex]\\ \sf\longmapsto x=6[/tex]
–20 ÷ 5 =
I need help
A 6-pound container of detergent costs $4.38. what is the price per pound?
Answer:
.73 per pound
Step-by-step explanation:
Take the total cost and divide by the number of pounds
4.38/ 6
.73 per pound
g A gift shop sells 40 wind chimes per month at $110 each. The owners estimate that for each $11 increase in price, they will sell 2 fewer wind chimes per month. Find the price per wind chime that will maximize revenue.
Answer:
The price that maximizes the revenue is $165
Step-by-step explanation:
We can model the price as a function of sold units as a linear relationship.
Remember that a linear relationship is something like:
y = a*x + b
where a is the slope and b is the y-intercept.
We know that if the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
For this line, we have the point (40, $110)
which means that to sell 40 units, the price must be $110
And we know that if the price increases by $11, then he will sell 2 units less.
Then we also have the point (38, $121)
So we know that our line passes through the points (40, $110) and (38, $121)
Then the slope of the line is:
a = ($121 - $110)/(38 - 40) = $11/-2 = -$5.5
Then the equation of the line is:
p(x) = -$5.5*x + b
to find the value of b, we can use the point (40, $110)
This means that when x = 40, the price is $110
then:
p(40) = $110 = -$5.5*40 + b
$110 = -$220 + b
$110 + $220 = b
$330 = b
Then the price equation is:
p(x) = -$5.5*x + $330
Now we want to find the maximum revenue.
The revenue for selling x items, each at the price p(x), is:
revenue = x*p(x)
replacing the p(x) by the equation we get:
revenue = x*(-$5.5*x + $330)
revenue = -$5.5*x^2 + $330*x
Now we want to find the x-value for the maximum revenue.
You can see that the revenue equation is a quadratic equation with a negative leading coefficient. This means that the maximum is at the vertex.
And remember that for a quadratic equation like:
y = a*x^2 + b*x + c
the x-value of the vertex is:
x = -b/2a
Then for our equation:
revenue = -$5.5*x^2 + $330*x
the x-vale of the vertex will be:
x = -$330/(2*-$5.5) = 30
x = 30
This means that the revenue is maximized when we sell 30 units.
And the price is p(x) evaluated in x = 30
p(30) = -$5.5*30 + $330 = $165
The price that maximizes the revenue is $165
rope price of length 45cm 25 cm and 81 cm have to be cut into same size pieces what is the smallest price length possible
= 2025
When you are told to find the smallest length possible, you perform L.C.M(Least common multiples)
For this, you divide the given lengths using the numbers that divides all through.
I have added an image to this answer. Go through it for more explanation
Assume a researcher wants to compare the mean Alanine Aminotransferase (ALT) levels in two populations, individuals who drink alcohol and individuals who do not drink alcohol. The mean ALT levels for the individuals who do not drink alcohol is 32 with a standard deviation of 14, and 37 individuals were in the sample. The mean ALT levels for individuals who drink alcohol is 69 with a standard deviation of 19, and 38 individuals were in the sample. Construct and interpret a 95% confidence interval demonstrating the difference in means for those individuals who drink alcohol when compared to those who do not drink alcohol.
a. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.22 and 39.78.
b. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.33 and 39.67
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
d. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.41 and 39.59.
Answer:
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
Step-by-step explanation:
Given :
Groups:
x1 = 69 ; s1 = 19 ; n1 = 38
x2 = 32 ; s2 = 14 ; n2 = 37
1 - α = 1 - 0.95 = 0.05
Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :
The confidence interval obtained is :
(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between
(24.32 ; 39.68) .
How would the following triangle be classified?
O scalene acute
O scalene obtuse
O isosceles acute
O isosceles obtuse
Answer:
isosceles acute
Step-by-step explanation:
We have two sides that are equal so the triangle is isosceles
None of the angles are larger than 90 degrees so non of the angles are obtuse, and none of the angles are 90 degrees, so the triangle is acute ( which means the angles are all less than 90 degrees)
