Using proportions, it is found that the speed of the sports car is of 85 miles per hour.
What is a proportion?A proportion is a fraction of a total amount.
The cars are moving in the same direction, hence their relative speed is the difference of them.
The sports car is 0.5 miles faster over one minute, hence over one hour the difference is:
60 x 0.5 = 30 miles per hour.
Considering that the utility vehicle has a speed of 55 mph, the speed of the sports car is given by:
55 + 30 = 85 miles per hour.
More can be learned about proportions at https://brainly.com/question/24372153
Claire invested $2,300 in an account paying an interest rate of
6
1
4
6
4
1
% compounded annually. Henry invested $2,300 in an account paying an interest rate of
6
3
4
6
4
3
% compounded monthly. To the nearest dollar, how much money would Claire have in her account when Henry's money has tripled in value?
Using compound interest, it is found that Claire will have $6,186 in her account when Henry's money has tripled in value.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.For Henry, we have that r = 0.0675, n = 12. The time it takes for the amount to triple is t when A(t) = 3P, hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]3P = P\left(1 + \frac{0.0675}{12}\right)^{12t}[/tex]
[tex](1.005625)^{12t} = 3[/tex]
[tex]\log{(1.005625)^{12t}} = \log{3}[/tex]
[tex]12t\log{(1.005625)} = \log{3}[/tex]
[tex]t = \frac{\log{3}}{12\log{(1.005625)}}[/tex]
t = 16.32.
Then, for Claire, we have that the parameters are as follows:
P = 2300, r = 0.0625, n = 1, t = 16.32.
Hence, the amount is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(t) = 2300\left(1 + \frac{0.0625}{1}\right)^{16.32}[/tex]
A(t) = 6186.
Claire will have $6,186 in her account when Henry's money has tripled in value.
More can be learned about compound interest at https://brainly.com/question/25781328
Please help me with this math problem!! :) Will give brainliest!!
Answer:
Step-by-step explanation:
2. Two angles are called?_ if they are not adjacent and their sides are formed by two intersecting lines.
Answer:
Vertical angles — two non-adjacent angles formed by two intersecting lines.
Step-by-step explanation:
An airplane flying at 650 miles per hour has a bearing of 54. After flying for 1.5 hours, how far north and how far east will the plane have traveled from its point of departure?
Answer:
627 miles north
747 miles east
Step-by-step explanation:
Bearing angles are measured east of north, so in (N, E) coordinates, the final position of the plane is ...
(1.5 h)(650 mi/h)(cos(50°), sin(50°)) = (975cos(50°), 975sin(50°)) mi
= (626.72, 746.89) mi
The plane will be 627 miles north and 747 miles east of its point of departure.
From the options below, choose the two triangles that are congruent
Find the volume 18in 7in 30in 12in
Answer:
1890 in³
Step-by-step explanation:
The formula to find the volume of a triangular prism: 1/2 x b x h x l, where b is the base, h is the height and l is the length.
1) Substitute the given values in the image into the formula above.
= 1/2 x 18 x 7 x 30
= 1/2 x 126 x 30
= 1/2 x 3780
= 1890
Delta Math: Angle Terminology with Equations
Answer:
m∠A = 139°
Step-by-step explanation:
Since knowing that:
Supplementary angles = 180 degree
Thus we put that in both equation:
( 7x - 15 ) + ( 2x - 3 ) = 180
Combine like terms & use inverse operations to find the value of x:
( 7x - 15 ) + ( 2x - 3 ) = 180
9x - 18 = 180
9x - 18 + 18 = 180 + 18
9x = 198
9x/9 = 198/9
x = 22
Hence, Angle A will have a measure of 7x - 15 which means 7 × 22 -15 = 154 - 15 = 139°
m∠A = 139°
The measure of Angle B will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°
m∠ B = 41°
Check Answer by add 139 and 31 which equal 180
~lenvy~
Sally's school is 2.5 km long. How many meters long is Sally's school
Answer: Sally's school is 2,500 meters long. Hope this helps!
Answer:
2500metres
Step-by-step explanation:
we all know that 1km is 1000 metres
so I take 1000metres×2.5km =2500HELP! WILL GIVE BRAINLEST!
Answer:
[tex]\frac{23\pi }{18}.[/tex]
Step-by-step explanation:
1) the rule of transformation [degr → rad] is:
[tex]\alpha [rad]=\alpha [degr] *\frac{\pi }{180};[/tex]
2) according to the formula above:
230°=230*π/180=23π/18 [rad].
Solve for v simplify your answer as much as possible: -2 + 3v = -23
Answer:
-7
Step-by-step explanation:
-2 + 3v = -23 >> -2 + 23 = -3v >> 21 = -3v >> v = -7
Answer:
V=-7
Step-by-step explanation:
To solve this equation, you must first add the -2 to both sides. (This cancels it out since you only want one variable on each side of the equation. It would be the other way around if the variable were positive) Now that you have the equation 3v=-21, you can divide. To get the v by itself, you must divide both sides by 3. This gives you the answer to the equation.
Hope this helps!!
How do you algebraically prove that two lines are parallel, and that two lines are perpendicular? Explain, and give a pair of equations for an example of each.
no explanation is needed :) please help
Answer:
187 in^2
Step-by-step explanation:
hope this helps!
What is the image point of (-4,8) after a translation right 4 units and up 2 units?
Answer:0,10
Step-by-step explanation: When translating you either add or subtract. If the problem says go down or to the left, you know that you will be subtracting, and if it says go up or to the right you will be adding. So up would add 4 to the x value which gives you 0 and you add 2 to the y value you get 10.
Answer:
(0, 10)
Step-by-step explanation:
-4 + 4 = 0
8 + 2
To verify, you can find the coordinates (0, 10) on a graph.
5 divided by 0.1960 long division
Answer:
5 divided by 0.1960 is 0.039
Step-by-step explanation:
0. 0 3 9
5 0. 1 9 6
− 0
0 1
− 0
1 9
− 1 5
4 6
− 4 5
1
Therefore 5 ÷ 0.1960 is 0.039
Location is known to affect the number, of a particular item, sold by an auto parts facility. Two different locations, A and B, are selected on an experimental basis. Location A was observed for 13 days and location B was observed for 18 days. The number of the particular items sold per day was recorded for each location. On average, location A sold 39 of these items with a sample standard deviation of 8 and location B sold 55 of these items with a sample standard deviation of 2. Select a 90% confidence interval for the difference in the true means of items sold at location A and B
We have two samples, A and B, so we need to construct a 2 Samp T Int using this formula:
[tex]\displaystyle \overline {x}_1 - \overline {x}_2 \ \pm \ t^{*} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} }[/tex]In order to use t*, we need to check conditions for using a t-distribution first.
Random for both samples -- NOT STATED in the problem ∴ proceed with caution!Independence for both samples: 130 < all items sold at Location A; 180 < all items sold at Location B -- we can reasonably assume this is trueNormality: CLT is not met; n < 30 for both locations A and B ∴ proceed with caution!Since 2/3 conditions aren't met, we can still proceed with the problem but keep in mind that the results will not be as accurate until more data is collected or more information is given in the problem.
Solve for t*:
We need the tail area first.
[tex]\displaystyle \frac{1-.9}{2}= .05[/tex]Next we need the degree of freedom.
The degree of freedom can be found by subtracting the degree of freedom for A and B.
The general formula is df = n - 1.
df for A: 13 - 1 = 12df for B: 18 - 1 = 17 df for A - B: |12 - 17| = 5Use a calculator or a t-table to find the corresponding t-score for df = 5 and tail area = .05.
t* = -2.015Now we can use the formula at the very top to construct a confidence interval for two sample means.
[tex]\overline {x}_A=39[/tex] [tex]s_A=8[/tex] [tex]n_A=13[/tex] [tex]\overline {x}_B = 55[/tex] [tex]s_B=2[/tex] [tex]n_B=18[/tex] [tex]t^{*}=-2.015[/tex]Substitute the variables into the formula: [tex]\displaystyle \overline {x}_1 - \overline {x}_2 \ \pm \ t^{*} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} }[/tex].
[tex]39-55 \ \pm \ -2.015 \big{(}\sqrt{\frac{(8)^2}{13} +\frac{(2)^2}{18} } } \ \big{)}[/tex]Simplify this expression.
[tex]-16 \ \pm \ -2.015 (\sqrt{5.1453} \ )[/tex] [tex]-16 \ \pm \ 3.73139[/tex]Adding and subtracting 3.73139 to and from -16 gives us a confidence interval of:
[tex](-20.5707,-11.4293)[/tex]If we want to interpret the confidence interval of (-20.5707, -11.4293), we can say...
We are 90% confident that the interval from -20.5707 to -11.4293 holds the true mean of items sold at locations A and B.
Pete makes 15 dollars an hour. He spends 25 dollars a day ontransportaon and food. Writean expression to describe hisspending and earnings in a day,where h is the number of hoursthat Pete works that day
a quadrilateral has exactly 2 congruent sides. wich quadrilateral types could it be? wich quadrilaterals could not be ?
y = x -5
x + y = -1
whats the soultion for the systeam of eqations
Answer:
x = 2
y = -3
Step-by-step explanation:
y = x - 5 -------------------(I)
x + y = -1 ----------------(II)
Substitute y = x -5 in equation (II)
x + (x - 5) = -1
x + x - 5 = -1 {Combine like terms}
2x - 5 = -1 {Add 5 to both sides}
2x = -1 + 5
2x = 4 {Divide both sides by 2}
x = 4/2
x = 2
Substitute x = 2 in equation (I)
y = 2 - 5
y = -3
A toy ball can be modeled as a sphere. Eva measures its diameter as 15.7 cm. Find the
ball's volume in cubic centimeters. Round your answer to the nearest tenth if necessary
Answer:
[tex]v = 2064.2 {cm}^{3} [/tex]
Step-by-step explanation:
we first consider the formula for the volume of a sphere
[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]
we were given diameter of 15.7cm.
we can find the radius by dividing the diameter by 2
because two times a radius makes a diameter.
[tex] \frac{15.7}{2} = 7.9cm[/tex]
we have the radius as 7.9cm.
and we know pi (π) to be 3.14 or 22/7.
but in this case, we use 3.14.
now let's substitute the values in the formula
[tex]v = \frac{4}{3} \times 3.14 \times {7.9}^{3} [/tex]
and we will get
[tex]v = 2064.19 {cm}^{3} [/tex]
but the nearest 10th will be
[tex]v = 2064.2 {cm}^{3} [/tex]
Answer: is 2026.3 cm ^3
Step-by-step explanation:
Distributed property 3(4x-5)
Answer:
Answer below!
Step-by-step explanation:
Alright I'm not too sure on what the question is asking for per your instructions, but I've written out my best explanation on how to use distributive property to solve this equation.
So first, what is the process of distributive property? It basically states whatever is in the parenthesis is multiplied by the outside number.
In simpler terms, each character in the parenthesis is multiplied by the number standing outside of the parenthesis.
So we can go...
(3 x 4x) - (3 x 5) = (12x) - (15)
And there's your answer, 12x - 15! Unless you know what x means, you'll probably just stop there.
Hope this was helpful!
The sum of two numbers is 15. One number is four times the other. Find the two numbers.
Answer:
12 and 3
Step-by-step explanation:
3 * 4 = 12
12 + 3 = 15
The sum of two numbers is -19. One number is 28 more than the other one. Find the numbers.
Answer:
-47
Step-by-step explanation:
28+ ___=-19
28+x= -19
-28 -28
_________
X= -47
28+-47= -19
Draw an area model. Then solve using the standard algorithm. 273 x 346.
Answer:
[tex]273*346=94,458[/tex]
Step-by-step explanation:
x 200 + 70 + 3
300 60,00 21,000 900 = 81,900
+ +
40 8,000 2,800 120 = 10,920
+ +
6 1,200 420 18 = 1,638
94,458
SOLUTION 6 Show that -0.75(-4f + 12) and (5f + 9) - (2f+ 18) are equivalent expressions.
[tex]-0.75(-4f+12)\\\\=-\dfrac 34(-4f +12)\\\\=-\dfrac 34 \cdot (-4f) - \dfrac 34\cdot(12)\\\\=3f-9\\\\\\(5f+9)-(2f+18)\\\\=5f+9-2f-18\\\\=3f-9\\\\\text{Hence, the expressions are equivalent.}[/tex]
2 1/2 x 2 1/4
Multiply, write the answer as a mixed number in the simplest form.
Answer:
5 1/2
Step-by-step explanation:
2x2=
4
2 x 1/2 =
1
2 x 1/4=
1/2
1+1/2=
1 1/2+4 =
5 1/2
in the figure below, what is the measure of angle x
Check the picture below.
PLSSSS HELP ME ASAP ILL GIVE YOU BRAINIEST!!!
Answer:
I believe it would be 8 11/20 ft³
Step-by-step explanation:
help me please. don't mine the blue dot on answer A.
Answer:
2 quarts .
Step-by-step explanation:
4 quarts make a gallon but two is already added
Answer:
2 quarts
Step-by-step explanation:
please help me it’s due today at 9:10am :(
I will give brainliest please help me
1) 720 inches³
2) 900 inches³
3) 120 inches³
hope it helps...!!!
Please HELP !! Find the SLOPE of the LINE
Answer: The slope is -2/1
Step-by-step explanation: We go 2 up and 1 to the left, meaning we get 2 over -1, to simplify, -2/1
Note: When we go down or to the left its negative, when we go up or to the right its positive
Answer: The slope is -2/1
Step-by-step explanation: