9514 1404 393
Answer:
B, D
Step-by-step explanation:
The volume is the product of the dimensions. For dimensions 9 ft, 9 ft, 10 ft, the volume is found by multiplying (9 ft) × (9 ft) × (10 ft) = 810 ft³.
To fill the volume with boxes of volume 1 ft³ would require 810 boxes.
H(x)=17+x/6 what is h(-18)=
Answer:
If h(x) = 17 + x/6, then h(-18) will equal to 14.
Step-by-step explanation:
We are given an equation...
h(x) = 17 + x/6
When you see h(x), the x represents the value that will be substituted in the equation. "For example, if you have h(9), then 9 would be your x-value." So, we are given h(-18) which means that -18 will be our x-value for this equation. Now that we know this, let's plug in this number into the equation.
h(x) = 17 + x/6
First, substitute the x-value which is -18.
h(-18) = 17 + (-18/6)
Next, divide -18 by 6.
h(-18) = 17 + (-3)
Since -3 is in front of a plus sign, then the equation would be like subtracting 3 from 17 so we will just replace the plus sign (+) with a minus sign (-).
h(-18) = 17 - 3
Now, subtract 3 from 17.
h(-18) = 14
Finally, you have your answer which is 14.
The value of H(x)=17+x/6 at H(-18) is 14.
What is function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.
given:
H(x)=17+x/6
Now, we have to find the value of the function at x= -18
So, H(-180= 17+ (-18)/6
H(-18)= 17 - 3
H(-18)= 14
hence, the value of H(-18) is 14.
Learn more about function here:
https://brainly.com/question/12431044
#SPJ5
Each of four tables at a party is set bowl with a bowl of grapes each Bowl contains 5/8 of a pound of grapes how many pounds of grapes are there altogether show your work
Answer:
2.5 pounds
Step-by-step explanation:
What’s the correct answer for this?
Answer:
ED = 26
Step-by-step explanation:
Using tangent-secant theorem
(12)²=(8)(x+10)
144=8x+80
144-80=8x
8x = 64
x=8
Now
ED = 8+8+10
ED = 26
Answer:
26
Step-by-step explanation:
Applying the tangent-secant theorem, we get:
12^2 = 8 * (x + 10)
144 = 8x + 80
= 8x = 144 - 80
8x = 64
x = 8
Putting x = 8 in ED, which is x + x + 10, we get:
= 8 + 8 + 10
= 26
Hope this helps!
Sarah Wiggum would like to make a single investment and have $1.7 million at the time of her retirement in 34 years. She has found a mutual fund that will earn 7 percent annually. How much will Sarah have to invest today
Answer:
Sarah has to invest $502,958.58 today.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex]
In this question:
[tex]t = 35, I = 0.07, T = 1700000[/tex]
She has to invest P today.
[tex]T = E + P[/tex]
[tex]1700000 = E + P[/tex]
[tex]E = 1700000 - P[/tex]
So
[tex]E = P*I*t[/tex]
[tex]1700000 - P = P*0.07*34[/tex]
[tex]3.38P = 1700000[/tex]
[tex]P = \frac{1700000}{3.38}[/tex]
[tex]P = 502958.58[/tex]
Sarah has to invest $502,958.58 today.
The hypotenuse of a 45°-45°-90° triangle measures 128 cm. A right triangle is shown. The length of the hypotenuse is 128 centimeters and the lengths of the other 2 sides are congruent. What is the length of one leg of the triangle? 64 cm 64 StartRoot 2 EndRoot cm 128 cm 128 StartRoot 2 EndRoot cm
Answer:
64√2 or 64 StartRoot 2 EndRoot
Step-by-step explanation:
A 45-45-90 traingle is a special traingle. Let's say one of the leg of the triangle is x. The other one is also x because of the isosocles triangle theorem. Therefore, using the pytagorean theorem, you find that x^2+x^2=c^2. 2(x)^2=c^2. You then square root both sides and get c= x√2.
Therefore, the two legs are x and the hypotenuse is x√2. x√2=128 because the question says that the hypotenuse is 128. Solve for x by dividing both sides by √2. X=128/√2. You rationalize it by multiplying the numberator and denominator of the fraction by √2. √2*√2= 2.
X=(128√2)/2= 64√2 cm.
Since X is the leg, the answer would be 64√2
Answer:
B.
Step-by-step explanation:
Which statement describes the graph of this polynomial function?
f(x) = x5-6x4+9x3
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
O The graph touches the x-axis at x = 0 and crosses the x-axis at x = 3.
O The graph crosses the x-axis at x = 0 and touches the x-axis at x = -3.
O The graph touches the x-axis at x = 0 and crosses the x-axis at x = -3.
Answer:
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
Step-by-step explanation:
When you graph this equation, you should see the zeros it passes and touches.
Answer:
A. The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
Step-by-step explanation:
The manufacturer of an airport baggage scanning machine claims it can handle an average of 560 bags per hour. (a-1) At α = .05 in a left-tailed test, would a sample of 16 randomly chosen hours with a mean of 538 and a standard deviation of 50 indicate that the manufacturer’s claim is overstated? Choose the appropriate hypothesis.
Answer:
The calculated value t = 1.76 < 2.131 at 0.05 level of significance
Null hypothesis is accepted
The manufacturer’s claim is greater than 560 bags per hour
Step-by-step explanation:
Explanation:-
Given sample size 'n' =16
Given the manufacturer of an airport baggage scanning machine claims it can handle an average of 560 bags per hour.
mean of the Population 'μ' = 560
Mean of the sample Χ⁻ = 538
sample standard deviation' S' = 50
Null hypothesis:H₀:μ > 560
Alternative Hypothesis:H₁ : :μ < 560 (left tailed test)
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{538-560 }{\frac{50}{\sqrt{16} } } = -1.76[/tex]
|t| = |-1.76| = 1.76
Degrees of freedom
γ = n-1 =16-1 =15
[tex]t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } =t_{0.025} =2.131[/tex]
Conclusion:-
The calculated value t = 1.76 < 2.131 at 0.05 level of significance
Null hypothesis is accepted
The manufacturer’s claim is greater than 560 bags per hour
Select the correct expression and value.
Ray has 3 boxes of chocolates. Each box has 4 layers of chocolates. Each layer has 4 rows of 4 chocolates each. He distributes all the chocolates equally among 16 friends. Identify the expression and the value that give the number of chocolates that each of Ray’s friends gets.
Answer:
Total chocolates= 48
Each friend get 3 chocolates
Step-by-step explanation:
Ray has 3 boxes of chocolates = 3
Each box has 4 layers of chocolates
= 4
Each layer has 4 rows of 4 chocolates each= 4
Total number of chocolates = 3*4*4
Total number of chocolates
= 48 chocolates
He shares 48 chocolates among 16 friends.
They Will all obtain 48/16= 3 chocolates each
Answer: the correct answer is 12
Please answer this math question im desperate!! thank you!! will give brainliest!!
Answer:
A
Step-by-step explanation:
It IS a function because it passes the vertical line test.
If you drew vertical lines through any part of the graph, it would only touch one point, showing that it is a function.
Talia tossed a penny many times. She got 20 heads and 55 tails. She said the experimental probability of getting heads was
20
55
. Explain and correct her error by completing the sentence. Enter your answer as a simplified fraction.
Answer:
For this case we know that in many times a penny shoes 20 head and 55 tails so then the total of trials are:
[tex] n = 20 +55=75[/tex]
Then we are interested in the probability of getting heads and if we use the Laplace formula we have:
[tex] p =\frac{Possible}{total}[/tex]
And the correct way would be:
[tex] p =\frac{20}{20+55}=\frac{20}{75}[/tex]
If we simplify we got:
[tex] p =\frac{4}{15}[/tex]
And the error was because she use 55 as the total number of trials and that's not the size of the sample space and for this reason she got [tex]\frac{20}{55}[/tex]
Step-by-step explanation:
For this case we know that in many times a penny shoes 20 head and 55 tails so then the total of trials are:
[tex] n = 20 +55=75[/tex]
Then we are interested in the probability of getting heads and if we use the Laplace formula we have:
[tex] p =\frac{Possible}{total}[/tex]
And the correct way would be:
[tex] p =\frac{20}{20+55}=\frac{20}{75}[/tex]
If we simplify we got:
[tex] p =\frac{4}{15}[/tex]
And the error was because she use 55 as the total number of trials and that's not the size of the sample space and for this reason she got [tex]\frac{20}{55}[/tex]
Answer the question above?
Answer:
m>n
Step-by-step explanation:
The value of m
The sum of the angles of a triangle are 180
50+30 + m = 180
m = 180-50-30
m = 100
The value of n
The sum of the angles of a triangle are 180
28 + 58+n = 180
n = 180-58-28
n=94
m>n
Which point satisfies both ƒ(x) = 2x and g(x) = 3x?
Answer:
(0,0)
Step-by-step explanation:
If a point satisfies both functions, they must be equal to each other. Thus, we have:
[tex]f(x)=g(x)[/tex]
[tex]2x=3x[/tex]
The only x that satisfies this is 0.
Therefore, the y is also zero.
The point is (0,0).
Alternatively, you can also visualize the graphs. The only point where the graphs will touch is the origin point or (0,0).
Write an equation of a circle with Center -5 -7 that through the point 0 0
Answer:
The third one, (x+5)^2 + (y+7)^2 = 74
Step-by-step explanation:
The equation for a circle is in the form (x-x coordinate)^2 + ( y - y coordinate )^2 = r^2
the radius is 5^2 + 7^2 = 25 + 49 = 74
and the center is (-5,-7), so it is + 5 and + 7
Question 6
An experiment consists of rolling a single die 12 times and the variablex is the number of times that the outcome is 6. Use binomial distribution to find the probability that the
outcome of 6 occurs exactly 3 times
Answer:
[tex] P(X=3)[/tex]
And using the probability mass function we got:
[tex] P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of times that 6 appears", on this case we now that:
[tex]X \sim Binom(n=12, p=1/6)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=3)[/tex]
And using the probability mass function we got:
[tex] P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974[/tex]
The circumference of a circle is 15 pi centimeters what is the area of the circle in terms of pi
Answer:
[225(pi)]/4
Step-by-step explanation:
circumference = pi(diameter)
area = pi (radius)^2
Diameter = 2(radius)
15pi cm = pi(diameter)
divide both sides by pi
diameter = 15
radius = 7.5
Area = pi (7.5)^2
A = 56.25 pi
most teachers prefer fractions so
225pi/4
Acar traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car can
Tavel on 7 gallons of gas?
637
m
633
m
63
m
Nnjkkk
Answer:
63 miles x miles
----------- = -------------
3 gallons 7 gallons
Step-by-step explanation:
We will use proportions. the number of miles over the gallons of gas
63 miles x miles
----------- = -------------
3 gallons 7 gallons
Answer: 147 miles
Step-by-step explanation:
On 3 gallons, he travelled 63 miles
On 7 gallons, he travels
7/3 x 63 = 147 miles
Many smartphones, especially those of the LTE-enabled persuasion, have earned a bad rap for exceptionally bad battery life. Battery life between charges for the Motorola Droid Razr Max averages 20 hours when the primary use is talk time and 7 hours when the Internet applications (The wall Street Journal, March 7, 2012).
Since the mean hours for talk time usage is greater than the mean hours for Internet usage, the question was raised as to whether the variance in hours of usage is also greater when the primary use Sample data showing battery hours of use for the two applications follows:
Primary use talking:
35.8 22.2 4.0 32.6 3.5 42.5
8.0 3.8 30.0 12.8 10.3 35.5
Primary use Internet:
24.0 12.5 36.4 1.9 9.9
5.4 1.0 15.2 4.0 4.7
a. Formulate hypotheses about the two population variances that can be used to determine if the population variance in battery hours of use is greater for the talk time application.
H1:σ21_____
Ha:σ22_____
b. What are the standard deviations of battery hours of use for the two samples? Round your answers to two decimal places.
S1_____
S2_____
c. Conduct the hypothesis test and compute the p-value.
- The value of _____
- P-value is _____
Answer:
Null hypothesis: the variance in hours of usage for talking is not greater than the the variance in hours of usage for internet.
[tex]H_o[/tex]: [tex]\sigma _1 ^2 \leq \sigma _2^2[/tex]
Alternative hypothesis: the variance in hours of usage for talking is greater than the the variance in hours of usage for internet.
[tex]H_a : \sigma_1^2 > \sigma_2^2[/tex]
[tex]\mathbf{s_ 1 =16.11}[/tex]
[tex]\mathbf{s_2 = 7.98}[/tex]
Step-by-step explanation:
Let [tex]x_1[/tex] and [tex]x_2[/tex] be the two variables that represents the battery life in hours for talking usage and battery life in hours for internet usage respectively.
The hypothesis can be formulated as:
Null hypothesis: the variance in hours of usage for talking is not greater than the the variance in hours of usage for internet.
[tex]H_o[/tex]: [tex]\sigma _1 ^2 \leq \sigma _2^2[/tex]
Alternative hypothesis: the variance in hours of usage for talking is greater than the the variance in hours of usage for internet.
[tex]H_a : \sigma_1^2 > \sigma_2^2[/tex]
The standard deviation for the battery usage for talking is :
[tex]\bar x_1 = \dfrac{1}{n_1} \sum x_i \\ \\ \bar x_1 = \dfrac{1}{12}(35.8 +22.4+...+35.5) \\ \\ \bar x_1 = \dfrac{241.2}{12} \\ \\ \bar x_1 =20.1[/tex]
The standard deviation Is:
[tex]s_ 1 = \sqrt{\dfrac{1}{n_1-1}\sum (x{_1i}-\bar x_i)^2}[/tex]
[tex]s_ 1 = \sqrt{\dfrac{1}{12-1}\sum (35.8- 20.1)^2+ (35.5-20.1)^2}[/tex]
[tex]s_ 1 = \sqrt{259.568}[/tex]
[tex]\mathbf{s_ 1 =16.11}[/tex]
The standard deviation for the battery life usage for the internet is :
[tex]\bar x_2 = \dfrac{1}{n_2} \sum x_{2i}[/tex]
[tex]\bar x_2 = \dfrac{1}{10} (24.0+12.5+36.4+...+4.7})[/tex]
[tex]\bar x_2 = \dfrac{115}{10}[/tex]
[tex]\bar x_2 = 11.5[/tex]
Thus; the standard deviation is:
[tex]s_2 = \sqrt{\dfrac{1}{n_2-1}(x_{2i}- \bar x_2)^2}[/tex]
[tex]s_2 = \sqrt{\dfrac{1}{10-1}(24-11.5)^2+(4.7-11.5)^2}[/tex]
[tex]s_2 = \sqrt{63.60}[/tex]
[tex]\mathbf{s_2 = 7.98}[/tex]
The spinner at the right is divided into eight equal parts. Find the theoretical probability of landing on the given section(s) of the spinner.
P(not less than 5)
Answer:
P(not less than 5) = 0.5
Step-by-step explanation:
Given
Parts of spinner = 8 equal parts
Required
P(not less than 5)
First, it'll be assumed that the parts of the spinner is numbered 1 - 8.
This gives the following sample space (S)
S = {1,2,3,4,5,6,7,8}
Total = 8
To calculate PP(not less than 5), the number of parts not less than 5 is needed.
Parts not less than 5 = {5,6,7,8}
Number of parts = 4
So, P(not less than 5) = Number of parts not less than 5 divided by total number of parts
Mathematically, P(not less than 5) = 4/8
P(not less than 5) = 4/8
P(not less than 5) = ½
P(not less than 5) = 0.5
Hence, the theoretical probability of PP(not less than 5) is 0.5.
Can someone help me figure out the steps to get the answer:)
Answer:
c = ± 8.363277
Step-by-step explanation :
[tex]5.72^{2} = 32.49\\\\6.12^{2} = 37.4544\\3.49 + 37.4544 = 69.9444\\\\c^{2} = \sqrt{69.9444} \\= 8.363277[/tex]
A stem and leaf plot shows data in _____ order.
alphabetical
numerical
reverse
Answer:
Numerical
because numerical order is an arrangement of a series of items by numbers in a sequential order.
how do you solve 6 1/4 x 2 7/11 =
Answer:
16 and 21/44 or 725/44
Step-by-step explanation:
convert 6 and 1/4 into an improper fraction; 25/4
convert 2 and 7/11 into an improper fraction; 29/11
multiply them together. [tex]\frac{25}{4}[/tex] × [tex]\frac{29}{11}[/tex]
you can do 25 × 29 to get 725
you can also do 4 × 11 to get 44.
725/44 simplifies to 16 and 21/44.
Alex was playing a board-game with a six-sided die. She tossed the die for her turn. What is the probability of 5?
Answer:
0.1667 = 16.67% probability of 5
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
The die can have 6 possible outcomes(1, 2, 3, 4, 5 and 6).
5 is one of the outcomes. So
p = 1/6 = 0.1667
0.1667 = 16.67% probability of 5
Given a triangle ABC such that AB = 4. AC = squareroot (41) and BC = 5.
Find the measures of the interior angles of ABC.
Answer:
A = 51.3°, B = 90°, C = 38.7°
Step-by-step explanation:
The given lengths satisfy the Pythagorean theorem:
(√41)² = 4² +5² ⇒ 41 = 16 +25
so we know the triangle is a right triangle. The right angle is opposite the longest side, so is angle B, opposite side AC.
The remaining angles can be found using trig functions. For example, we know ...
tan(A) = BC/AB = 5/4
A = arctan(5/4) ≈ 51.3°
Then the other acute angle is ...
C = 90° -51.3° = 38.7°
Angles A, B, C are ...
(A, B, C) = (51.3°, 90°, 38.7°)
PLEASE HELP 20 POINTS + BRAINLIEST IF ANSWERED Which method correctly solves the equation using the distributive property? Negative 0.2 (x minus 4) = negative 1.7 Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x minus 4 = negative 1.7. Negative 0.2 x = 2.3. x = negative 11.5. Negative 0.2 (x minus 4) = negative 1.7. x minus 4 = 0.34. x = 4.34. Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x + 0.8 = negative 1.7. Negative 0.2 x = negative 2.5. x = 12.5. Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x minus 0.8 = negative 1.7. Negative 0.2 x = negative 0.9. x = 4.5.
Answer:
i would say B
hope i could help
Answer:
B is the answer
Step-by-step explanation:
A graphic designer wants to translate rectangle DEFG using T–1, 2(x, y). The pre-image has coordinates D(–1, 3),
E(4, 3), F(4, 1), and G(–1, 1). What is the image of DEFG?
Answer:
D'(-2, 5), E'(3, 5), F'(3, 3), G'(-2, 3)
Step-by-step explanation:
Adding (-1, 2) to each of the coordinates gives ...
D +(-1, 2) = (-1-1, 3+2) = D'(-2, 5)
E +(-1, 2) = (4-1, 3+2) = E'(3, 5)
F +(-1, 2) = (4-1, 1+2) = F'(3, 3)
G +(-1, 2) = (-1-1, 1+2) = G'(-2, 3)
Answer:
The answer is B.
Step-by-step explanation:
I got it correct on Edge 2020
A University of Florida economist conducted a study of Virginia elementary school lunch menus During the state-mandated testing period, school lunches average 863 calories The economist claims that after the testing period ends, the average caloric content of Virginia school lunches drops significantly They collected a random sample of 500 students' school lunches around Virginia
a). What null and alternative hypotheses should you test?
b). Set up the rejection region for this study using alpha = 0.05 Interpret alpha = 0.05 in the words of the problem
c). Suppose the sample data yielded the test statistic z = -2.17 What conclusion can you draw for the test?
d). Calculate the observed p-value for the test statistic z = -2.17 Interpret the p-value and draw the conclusion based on it
Answer:
a) Null hypothesis: [tex] \mu \geq 863[/tex]
Alternative hypothesis: [tex] \mu >863[/tex]
b) For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:
[tex] z_{\alpha}=-1.64[/tex]
And the rejection zone would be:
[tex] z<-1.64[/tex]
c) For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance
d) [tex] p_v = P(z<-2.17) =0.015[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided
Step-by-step explanation:
Part a
We want to test for this case if the true mean is significantly less than 863 calories so then the system of hypothesis are:
Null hypothesis: [tex] \mu \geq 863[/tex]
Alternative hypothesis: [tex] \mu >863[/tex]
Part b
For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:
[tex] z_{\alpha}=-1.64[/tex]
And the rejection zone would be:
[tex] z<-1.64[/tex]
Part c
For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance
Part d
For this case the p value would be given by:
[tex] p_v = P(z<-2.17) =0.015[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided
Please answer this correctly
Answer:
7.07
Step-by-step explanation:
The area of the whole circle is given by the formula ...
A = πr^2
For the given values, the area of the circle is ...
A = 3.14(3 in)^2 = 28.26 in^2
One-quarter of that area is ...
(28.26 in^2)/4 = 7.065 in^2
The area of the quarter-circle is about 7.07 square inches.
Answer:
[tex] = 7.065 {in}^{2} [/tex]
Step-by-step explanation:
[tex] area = \frac{90}{360} \times \pi {r}^{2} \\ \frac{1}{4} \times 3.14 \times 3 \times 3 \\ = \frac{28.26}{4} \\ = 7.065 \: \: {in}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Let X and Y be independent normal random variables with distributions X „ Np1, 3q and Y „ Np0, 4q. Let W " 1 2X ´ Y ` 6. (a) Identify the distribution W. (b) Find the probability PpW ą 6q.
Answer:
Step-by-step explanation:
Here we have,
E(X) = 1, var(X) = 3, E(Y) = 0, var(Y) = 4
Since X and Y has normal distribution so W will also have normal distribution with mean
E(W) = E(05X-Y+6)
= 0.5E(X) - E(Y) +6
= 0.5* 1 -0+ 6
= 6.5
and variance
Var(W) = Var(0.5X-Y+6)
= 0.25Var(X)+Var(Y)
= 0.25 * 3 + 4
= 4.75
(b)
The z-score for W = 6 is
[tex]z=\frac{6-6.5}{\sqrt{4.75} } \\\\=-0.23[/tex]
The required probability is:
P(W>6) = P(z > -0.23)
= 0.5910
A typist can type 45 words per minute. How many minutes will it take him the type a 2500 word report?
Answer:
55.56 or 55 5/9
Step-by-step explanation:
To find the time it takes to type a report, you need to divide the number of words in the report by the words the typist can type in a minute.
2500/45 = 55.56
It takes 55.56 minutes or 55 5/9 minutes to type a 2500 word report.
Answer:
55 minutes and 33 seconds.
Step-by-step explanation:
To solve this we can set up a proportion.
1/45=x/2500
Cross multiply.
1*2500=45*x
45x=2500
Divide both sides by 45.
x=55.5*
.5* minutes is about 33 seconds. (0.55555*60)
So, it will take him around 55 minutes and 33 seconds.
Lila flies a drone in the direction of 90° towards Avery. Once she gets to Avery she changes course and flies in the direction of 200° towards Mark. Lila and Avery are 20 feet apart; Mark and Avery are 30 feet apart. How far apart are Mark and Lila?
Answer: 29.8ft
Step-by-step explanation:
suppose that the angles are measured from an x-axis.
we know that:
Lila and Avery are 20 feet apart.
Mark and Avery are 30 feet apart.
If we locate the position of Lila in the (0, 0)
and we use the relation:
x = r*cos(θ) and y = r*cos(θ)
Then the position of Avery is:
P = (20ft*cos(90°), 20ft*sin(90°)) = (0, 20ft)
and the position of mark will be:
P = (0 + 30ft*cos(200°), 20ft + 30ft*sin(300)) = (-28.2ft, 9.7ft)
And because Lila is at the origin, the distance between Mark and Lila is equal to the module of that vector,
Distance = √((28.2ft)^2 + (9.7ft)^2) = 29.8ft
