April shoots an arrow upward at a speed of 80 feet per second from a platform 25 feet high. The pathway of the
arrow can be represented by the equation h = -16t2 + 80t + 25, where h is the height and t is the time in
seconds. What is the maximum height of the arrow?
90 feet
140 feet
125 feet
80 feet
Answer:
The maximum height of the arrow is 125 feet.
Step-by-step explanation:
The pathway of the arrow can be represented by the equation,
[tex]h = -16t^2 +80t + 25[/tex] .....(1)
Where h is height in in feet and t is time in seconds.
It is required to find the maximum height of the arrow. For maximum height, [tex]\dfrac{dh}{dt}=0[/tex].
So,
[tex]\dfrac{d(-16t^2 +80t + 25)}{dt}=0\\\\-32t+80=0\\\\t=\dfrac{80}{32}\\\\t=2.5\ s[/tex]
Put t = 2.5 s in equation (1). So,
[tex]h = -16(2.5)^2 +80(2.5) + 25\\\\h=125\ \text{feet}[/tex]
So, the maximum height of the arrow is 125 feet.
What is the surface area?
Answer:
416 square yards
Step-by-step explanation:
The formula for the surface area of the 2 bases is just b*h
12*8=96 yd²
Finding the lateral area:
(10*10)+(10*10)+(12*10)=
100+100+120=
320 yd²
Add the lateral surface area and the surface area of the 2 bases for the total surface area:
320+96=416 yd²
Zoe walked 9 miles in 6 hours. what was her walking rate in miles per hour? put it in simplest form
Answer:
1.5
Step-by-step explanation:
quadratic formula 2x^2+7x-15=0
Answer:
Step-by-step explanation:
I hope this was what you were looking for. Have a nice day!
Answer:
x= 3 /2 , x=−5
(2x−3)(x+5)=0
Step 2: Set factors equal to 0.
2x−3=0 or x+5=0
Avery earned $68 at her job when she worked for 8 hours. What was her hourly pay rate in dollars per hour? Express your answer in simplest form.
Answer:
$8.5
Step-by-step explanation:
divide 68.00 by 8
What is the slope of the line y=4x-2 ?
Answer:
4
Step-by-step explanation:
The slope will always be x's coefficient, or the number attached to x.
That's slope intercept form y = mx + b, where m is the slope, so we just read off the answer.
Answer: 4
Do the following angle measures make a triangle: 88°, 16°, 65°?
Jerome solved the equation 1
3
x + 5
6
= 1 as shown.
1. Subtraction property
of equality: 1
3
x + 5
6
− 5
6
= 1
1
− 5
6
2. LCD: 1
3
x = 1
6
− 5
6
3. Multiply by the
reciprocal: ( 3
1
) 1
3
x = −4
6
( 3
1
)
4. Solve and simplify: x = −12
6
= −2
Analyze Jerome’s steps. In which step did he make an error?
In step 1, he needed to add StartFraction 5 Over 6 EndFraction to both sides of the equation.
In step 2, the LCD was not used correctly to make equivalent fractions.
In step 3, the correct reciprocal was not multiplied to both sides.
In step 4, the answer was not reduced correctly.
Answer:
B (second option)
Step-by-step step 2, the LCD was not used correctly to make equivalent fractions.
Answer:
the answer is b
Step-by-step explanation:
got it right
A poll is given, showing 45% are in favor of a new building project.
If 3 people are chosen at random, what is the probability that exactly 1 of them favor the new building project?
The probability of exactly 1 person favoring the new building project out of 3 people chosen at random is approximately 0.4083, or 40.83%.
Use the concept of probability defined as:
Probability is the ratio of the number of favorable outcomes to the total number of outcomes for the occurrence of an event.
Given that,
A poll was conducted on a new building project.
The results of the poll represent 45% of the respondents were in favor of the new building project.
To calculate the probability that exactly 1 person favoring the new building project out of 3 people chosen at random:
Use the binomial probability formula:
[tex]P(X=k) = (^nC_k) p^k (1-p)^{(n-k)}[/tex]
Where P(X=k) is the probability of getting exactly k favorable responses, and n is the total number of people chosen.
In this case, n = 2,
k is the number of favorable responses, in this case, 1,
p is the probability of an individual favoring the new building project in this case, 0.45,
And (1-p) is the probability of an individual not favoring the new building project in this case, 0.55.
Now substitute the values into the formula:
[tex]P(X=1) = (^3C_1) (0.45^1) (0.55^{(3-1)})[/tex]
Calculating the values:
[tex]^3C_1 = 3[/tex]
(which represents the number of ways to choose 1 favorable response out of 3 people),
[tex]0.55^{(3-1)} = 0.3025.[/tex]
Substituting these values back into the formula:
P(X=1) = (3)(0.45)(0.3025)
Calculating further:
P(X=1) = 0.4083
Hence,
The probability of exactly 1 person favoring the new building project out of 3 people chosen at random is approximately 0.4083, or 40.83%.
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Final answer:
The probability of exactly 1 out of 3 individuals favoring a new building project is 40.35%.
Explanation:
The probability of a person favoring a new building project is 45%.
To find the probability that exactly 1 out of 3 chosen individuals favor the project, we use the binomial probability formula:
Calculate the probability of 1 person favoring the project: 0.45 * 0.55 * 0.55 = 0.1345
Calculate the number of ways 1 person can be chosen out of 3: 3 choose 1 = 3
Multiply the two results: 3 * 0.1345 = 0.4035
Therefore, the probability that exactly 1 out of 3 individuals favor the new building project is 0.4035 or 40.35%.
Find the value of z.
Answer:
[tex]60 \: degrees[/tex]
Step-by-step explanation:
[tex]180(n - 2)[/tex]
you have to put the number of sides for n
[tex]180(n - 2) \\ 180(6 - 2) \\ 180 \times 4 \\ = 720[/tex]
720 is the sum of interior angles. so to find the value of an angle you have to divide 720 by the number of angles.
[tex] \frac{720}{6} = 120 \: \: degrees[/tex]
we know that,
interior angle + exterior angle = 180 degrees
[tex]120 + z = 180 \\ z = 180 - 120 \\ z = 60 \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Leah wants to see a castle in an amusement park. She sites the top of the castle at an angle of elevation of 45°. If she knows the castle is $160 from her how tall is the castle prom at her level of vision?
Answer:
x=236 feet
Step-by-step explanation:
please help me find the distance between the point (2,5) and (5,9)
Answer:
5 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (2, 5) and (x₂, y₂ ) = (5, 9)
d = [tex]\sqrt{(5-2)^2+(9-5)^2}[/tex]
= [tex]\sqrt{3^2+4^2}[/tex]
= [tex]\sqrt{9+16}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
find the percentage of 25 cents of $2.00
Answer:
[tex]12.5%[/tex]%
Step-by-step explanation:
[tex]\frac{25}{200}[/tex] is simplified to [tex]\frac{1}{8}[/tex], which in "perfect form," is [tex]12.5%[/tex]%
Answer:
12.5%
Step-by-step explanation:
$2 = 200c
200c ........ 100%
25c ................x%
x = 25×100/200
= 25/2
= 12.5%
how many ounces are in 3 pounds
Answer:
48
Step-by-step explanation:
16*3
16 oz in a pound
what is the perimeter of this tile 4in 1in
Answer:
10 inches
Step-by-step explanation:
Assuming a rectangular tile
P = 2(l+w) where l is the length and w is the width
P = 2(1+4)
= 2(5)
= 10 inches
Answer:
10 in
Step-by-step explanation:
Sunita creates a scale model of an aeroplane. The scale of the model is 5 cm to 13 m. Sunita's model has a wingspan of 24 cm. What is the wingspan of the real aeroplane?
To find the wingspan of the real aeroplane, we use the scale of 5 cm to 13 m and set up a proportion comparing the model's wingspan of 24 cm with the real wingspan, which results in a real wingspan of 62.4 m.
Sunita's scale model of an aeroplane has a wingspan of 24 cm, and the scale used is 5 cm to 13 m. To find the wingspan of the real aeroplane, we set up a proportion where 5 cm on the model represents 13 m in reality. The ratio would be:
Model scale: 5 cm
Real scale: 13 m = 1300 cm (since 1 m = 100 cm)
Now we find the corresponding real-life measurement for the 24 cm wingspan on the model:
(5 cm / 1300 cm) = (24 cm / Wingspan in cm)
To solve for the real wingspan, we cross-multiply and divide:
5 cm * Wingspan in cm = 1300 cm * 24 cm
Wingspan in cm = (1300 cm * 24 cm) / 5 cm
Wingspan in cm = 31,200 cm / 5 cm
Wingspan in cm = 6,240 cm
Converting back to meters (divide by 100 since 1 m = 100 cm):
Wingspan in m = 6,240 cm / 100 = 62.4 m
what is the answer for this question y/15 = 8 plz help fast
What is the median?
Answer:
-4.5
Step-by-step explanation:
Order this from least to greatest.
-8, -6, -5, -4, -3, -3
find the middle.
median = (-5 + -4)/2 = -9/2 = -4.5
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{\dfrac{-3 + -8 + -4 + -3 + -5 + -6}{6}}[/tex]
[tex]\mathsf{-3 + -8 + -4 + -3 + -5 + -6}[/tex]
[tex]\mathsf{= -3 - 8 - 4 - 3 - 5 - 6}[/tex]
[tex]\mathsf{-3 - 8 = \boxed{\large\textsf{\bf -11}}}[/tex]
[tex]\mathsf{ -11 - 4 - 3 - 5 - 6}[/tex]
[tex]\mathsf{-11 - 4 = \boxed{\large\textsf{\bf -15}}}[/tex]
[tex]\mathsf{-15 - 3 - 5 - 6}[/tex]
[tex]\mathsf{-15 - 3 =\boxed{\large\textsf{\bf -18}}}[/tex]
[tex]\mathsf{-18 - 5 - 6}[/tex]
[tex]\mathsf{-18 - 5 = \boxed{\large\textsf{\bf -23}}}[/tex]
[tex]\mathsf{-23 - 6}[/tex]
[tex]\mathsf{= \boxed{\large\textsf{\bf -29}}}[/tex]
[tex]\mathsf{= \dfrac{-29}{6}}[/tex]
[tex]\mathsf{= \boxed{-4.83333333333}}[/tex]
[tex]\boxec{\boxed{\large\textsf{Answer: \bf -4.83333333333 or }\mathsf{\bf \dfrac{-29}{6}\large\textsf{ both should work they both}}}}\\\boxed{\large\textsf{equal the same thing!}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A cylinder with radius 5 units is shown below. It’s volume is 157 cubic units.
Answer: 2 units
Step-by-step explanation:
Volume = π r² h
157 = π (5)² h
h = 157 ÷ 25π
h = 2 units.
The cable company is analyzing data from two satellite television providers to determine whether their users spend more time watching live television or shows that have been recorded. Satellite Company X : 89 live, 430 recorded Satellite Company Y : 65 live, 94 recorded What is the probability that a randomly selected customer from Company Y watches recorded shows more often than live television? Give your answer in percent form rounded to the nearest whole percent.
Answer:
59%
Step-by-step explanation:
The information from Satellite Company Y is:
65 people watch live and 94 people watch recorded.
The total number of people from Y is:
65 + 94 = 159
So the probability that a random person from Y watches recorded shows more often is given by the division of the number of people watching more recorded shows (94) over the total number of people (159):
Probability = 94 / 159 = 0.5912 = 59.12%
Rounding to nearest whole percent, we have 59%
Answer:
59%
Step-by-step explanation:
I got 100%
What is the area of triangle PQR? Triangle P Q R has a base of 86 inches and a height of 52 inches. 1,118 square inches 2,236 square inches 2,322 square inches 3,870 square inches
Answer:
2,236 square inches
Step-by-step explanation:
A=86*52/2=2,236 square inches
The area of triangle PQR which has a base of 86 inches and a height of 52 inches is 2,236 square inches.
What is the area of a triangle?The area of the triangle is the space occupied by it on the two-dimensional plane. The area of the triangle is half of the product of its base and height.
[tex]A=\dfrac{1}{2}bh[/tex]
Here, (b) is the base of the triangle and (h) is the height.
Triangle PQR has
A base of 86 inches A height of 52 inches.Put these values in the above formula to find the area of the triangle PQR as,
[tex]A=\dfrac{1}{2}(86\times52)\\A=2236\rm\; in^2[/tex]
Hence, the area of triangle PQR which has a base of 86 inches and a height of 52 inches is 2,236 square inches.
Learn more about the triangle here;
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The layers of a rectangular prism are shown below.
Answer:
18 Cubic cm
Step-by-step explanation:
Count all of the squares granted one cube = 1 cm^3, there are 18 cubes so it would be 18cm^3
Simplify the expressions (with work please)
1. 4 - (-3)
2. 1/6 + 7/12
3. 0.24 - 1.6
4. 2 3/5 x (-4/3)
5. -24 divided by 3.2
Answer:
Read below. Answers are bolded for you.
Step-by-step explanation:
1. 4-(-3)=4+3=7 (a negative and a negative is a positive)
2. 1/6 + 7/12=[tex]\frac{2}{12} +\frac{7}{12} =\frac{9}{12} =\frac{3}{4}[/tex] or 3/4
3. 0.24 - 1.6= -1.36
4. 2 3/5 x (-4/3)= [tex]2 \frac{3}{5} * -\frac{4}{3} =\frac{13}{5} *-\frac{4}{3} =-\frac{52}{15} =-3\frac{7}{15}[/tex] or -3 7/15
5. -24÷3.2=-7.5
Answer:
1. 7
2. 0.75
3. -1.36
4. -52/15
5. -7.5
Step-by-step explanation:
1. 4 - ( -3 ) = 4 + 3 = 7
2. 0.166 + 0.583 = 0.749 (round to the nearest hundredth) 0.75
3. 0.24 - 1.6 = 0.24 + -1.6 = -1.36
4. 13/5 * (-4/3) (easiest to multiply as not mixed fractions) = -52.15
-24 / 3.2 (think about -24 / 3 = -7 and -24 / 0.2 = -0.5 (-7 + -0.5)) = -7.5
I hope this helps lots! ^^
A bag contains four yellow marbles, six red marbles, five blue marbles, six white marbles, and four black marbles. What is the theoretical probability of pulling a white marble from the bag?
Answer is 6/25
because you have to add all the marbles wich will be:
four yellow marbles, six red marbles, five blue marbles, six white marbles, six white marbles
4 + 6 + 5 + 6 + 4 = 25
so there is 6 white marbles and a total of 25 marbles so it will be 6/25
have a nice day!
also can you please give me brainliest :)
Suppose a soup can has a diameter of 10cm and a height of 12cm what is the volume of the soup in the can
Answer: 942.48 [tex]Units ^{3}[/tex]
Step-by-step explanation:
First we find the area of the base (the circle) the formula for that is [tex]\pi r^{2}[/tex]
the radius is 5 because it is half the diameter.
so our base is 78.54
then we multiply that by the height
so 78.54 times 12 = 942.48
a line passes through the point (10, -2) and had a slope of -1/2. write an equation in point-slope form for this line.
y+2=-1/2(X-10)
y=1/2X -5-2
Y=1/2X -7
What is the unit price for $175 for 4 concert tickets?
Answer:
Answer: Each ticket cost $63
Step-by-step explanation:
The Reyes family bought 4 tickets
The total cost is $252
So that means you have to divide $252 by the amount of tickets bought which is 4
$252÷4=$63
Answer:
$43.75
Step-by-step explanation:
175/4= 43.75
There is a bag filled with 6 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 red?
The probability of getting exactly 1 red marble is 60/121.
Given data:
To find the probability of getting exactly 1 red marble, we need to consider the two possible scenarios:
Getting a red marble on the first draw and a blue marble on the second draw.
Getting a blue marble on the first draw and a red marble on the second draw.
The probability of getting a red marble on the first draw is 5/11, since there are 5 red marbles out of a total of 11 marbles in the bag.
The probability of getting a blue marble on the second draw is also 6/11, since we replace the marble after the first draw, so the number of marbles remains the same.
The probability of the first scenario occurring is (5/11) * (6/11) = 30/121.
Similarly, the probability of the second scenario occurring is (6/11) * (5/11) = 30/121.
To find the total probability of getting exactly 1 red marble, we add the probabilities of these two scenarios:
Total probability = (30/121) + (30/121)
= 60/121.
Hence, the probability of getting exactly 1 red marble is 60/121.
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The probability of drawing exactly one red in two draws, considering the order, is the sum of the two scenarios: 'red then blue' and 'blue then red'. Here, the total probability is calculated as (5/11 * 6/11) + (6/11 * 5/11).
Explanation:The question presented falls under the concept of probability in Mathematics. We have a bag with 6 blue and 5 red marbles. A marble is chosen, its color is recorded, and then it is put back in the bag before another marble is chosen. Thus, the color of the first marble selected does not have any influence on the color of the second marble because of replacement.
To get the probability of drawing one red marble in two attempts, we can consider two possibilities: either the first draw is red and the second is blue, or the first draw is blue and the second is red.
Scenario 1: The first marble drawn is red and the second marble drawn is blue. The probability of drawing a red marble on the first attempt is 5/11, since there are 5 red marbles out of a total of (6+5)=11 marbles. After replacing the first marble, the probability of drawing a blue marble on the second try is 6/11. Therefore, the total probability for this possibility is the product of both individual probabilities: (5/11) * (6/11).
Scenario 2: The first marble drawn is blue and the second marble drawn is red. The probability is calculated in the same manner resulting into (6/11) * (5/11).
Finally, to get the total probability of drawing exactly one red marble in two draws, we add the probabilities for the two scenarios: (5/11 * 6/11) + (6/11 * 5/11).
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Can you guys create your own system of equations word problem, define the variable, write an equation, then solve it and make a sentence explanation on why you did what you chose
Thanks will give brainliest
Answer:
Using a system of equations, however, allows me to use two different variables for the two different unknowns.
number of adults: a
number of children: c
With these variables, I can create equations for the totals they've given me:
total number: a + c = 2200
total income: 4a + 1.5c = 5050
Now I can solve the system for the number of adults and the number of children. I will solve the first equation for one of the variables, and then substitute the result into the other equation:
a = 2200 – c
4(2200 – c) + 1.5c = 5050
8800 – 4c + 1.5c = 5050
8800 – 2.5c = 5050
–2.5c = –3750
c = 1500
Now I can back-solve for the value of the other variable:
a = 2200 – (1500) = 700
I have values for my two variables. I can look back at my definitions for the variables to interpret these values. To answer the original question, there were:
1500 children and 700 adults.
Final answer:
A word problem involving two people and their apples, where Alice has twice as many apples as Bob. The variables are defined, the equation is written, and the solution is found.
Explanation:
Word Problem:
Alice has twice as many apples as Bob. Together, they have 15 apples. Define the variable 'x' as the number of apples Bob has.
Equation:
Alice's apples: 2x
Bob's apples: x
2x + x = 15
Solution:
Combining like terms: 3x = 15
Dividing both sides by 3: x = 5
Sentence Explanation:
We defined the variable 'x' as the number of apples Bob has. Since Alice has twice as many apples, we expressed her number of apples as 2x. The total number of apples they have together is 15, so we created an equation by summing up both Alice's and Bob's apples. By solving for 'x', we found that Bob has 5 apples.
Deanna gets 3 problems incorrect on her math quiz and scores 85%. How many questions were on the quiz?
Answer:
There were 20 questions on the quiz
Step-by-step explanation:
In this question, we are concerned with knowing the number of questions on a quiz, given that Deana had a certain percentage after scoring an amount of marks.
We proceed as follows;
Let the number of questions on the quiz be X.
Now, she got 85% by making 3 incorrect choices. This means the percentage of questions she got incorrectly would be 100-85 = 15%
what we are saying is that it is just 15% of her questions that were wrong.
This mathematically;
15% of x = 3
15/100 * x = 3
15x = 3 * 100
15x = 300
x = 300/15
x = 20