Answer:
Time taken to reach maximum height=0.875 seconds
Maximum height = 78.25 ft
Step-by-step explanation:
The function which models the height of the ball is given as:[tex]s(t)=-16t^2+28t+66[/tex]
The function s(t) reaches its maximum height at the axis of symmetry. For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex], the axis of symmetry occurs at [tex]x=-\frac{b}{2a}[/tex].
In s(t), a=-16, b=28
[tex]t=-\frac{28}{2(-16)}=0.875 seconds[/tex]
The ball reaches its maximum height after 0.875 seconds
(b)Maximum Height
Given [tex]s(t)=-16t^2+28t+66[/tex]
At t=0.875
[tex]s(0.875)=-16(0.875)^2+28(0.875)+66=78.25 ft[/tex]
Maximum height = 78.25 ft
Answer:
time: 0.875 seconds
maximum height: 18.25 feet
Step-by-step explanation:
The function that gives the height of the ball in feet after t seconds is:
s(t) = −16t^2 + 28t + 6
The inicial velocity is 28 ft/sec, and the inicial position is 6 feet.
So, to find the time when the ball reaches the maximum heigth, we need to find the vertix of the equation −16t^2 + 28t + 6.
We can use the following formula to find it:
t_vertix = -b/2a
where a and b are coefficients of the quadratic equation (in our case, a = -16 and b = 28).
So, we have that:
t_vertix = -28/(-32) = 0.875 seconds
To calculate the maximum height we just need to use this time in the equation of position:
s(0.875) = −16*(0.875)^2 + 28*0.875 + 6 = 18.25 feet
simplify (x -3)(x + 7) using the table method, and identify the resulting expression in standard form.
Answer the question please I don’t get it either
Answer:
The top angle is 60 degrees
Step-by-step explanation:
Triangle angle sum equals to 180. 90 plus 30 is 120 and when you subtract that from 180 tada! 60
A green die and a red die are tossed. What is the probability that a "4" shows on the green die and a "5" shows on the red die?
Answer:
1 out of 6 for green die and 1 out of 6 for red die
Step-by-step explanation:
As we know there are six numbers on both of the dices
so if we toss a die there is a 1 out of 6 outcomes that a 4 comes out for the green die and 1 out of 6 outcomes again for the red die
The probability that a 4 shows on the green die and a 5 shows on the red die is given by P ( C ) = 1/36
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that a 4 shows on the green die and a 5 shows on the red die be represented as P ( C )
Now , the number of outcomes in a roll of die = { 1 , 2 , 3 , 4 , 5 , 6 } = 6 outcomes
And , probability that a 4 shows on the green die P ( A ) = 1/6
The probability that a 5 shows on a red die P ( B ) = 1/6
Now , it is an independent experiment
So , the compound probability is P ( C ) = P ( A ) . P ( B )
And , the probability that a 4 shows on the green die and a 5 shows on the red die P ( C ) = ( 1/6 ) ( 1/6 )
The probability that a 4 shows on the green die and a 5 shows on the red die P ( C ) = 1/36
Hence , the probability is P ( C ) = 1/36
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Angles! It's Urgent Pleasee help me
Answer:
<1 and <2 are alternate exterior angles
<3 and <4 are consecutive interior angles
Step-by-step explanation:
<1 and <2 are alternate exterior angles
Alternate exterior angles are on opposite outside of the lines
<3 and <4 are consecutive interior angles
Consecutive interior angles are on the same side on the inside of the line
need geometry help asap!
image above✨
For a school fundraiser, Ayana needs to sell 40 rolls of wrapping paper. So far, she has sold 7 rolls to her grandmother, 2 rolls to her uncle, and 9 rolls to a neighbor. How many more rolls of wrapping paper does Ayana need to sell?
Answer:
22?
Step-by-step explanation:
Just take 40 and subtract the 7 to get 33 and then 2 to get 31 and 9 to get 22.
Answer:
22 more rolls
Step-by-step explanation:
if she needs to sell 40 and she has sold 9+7+2=18 than you subtract 18 from 40 getting 22 more rolls
Consider a system to be one train car moving toward
another train car at rest. When the train cars collide, the
two cars stick together.
What is the total momentum of the system after the
collision?
800 kg. m
1,600 kg. m
2,400 kg. m
4,000 kg. m
Step-by-step explanation:
I just finished the assignment and got everything right ;)
Hope i helped!
Answer:
c
Step-by-step explanation:
6x squared plus 2x minus 20 equals 0
Answer:
x=2 or 5/3
Step-by-step explanation:
the explanation is in the picture
please like and Mark as brainliest
Answer:
x = 5/3
x = -2
Step-by-step explanation:
6x² + 2x - 20 = 0
(6x - 10)(x + 2)
= 6x² + 12x - 10x - 20
= 6x² + 2x - 20
6x - 10 = 0
6x = 10
x = 10/6
x = 5/3
x + 2 = 0
x = -2
One of the largest cookies on record had a diameter of 78.75 feet. What is the approximate circumference of the cookie? Use 3.14 for n. Round to tenths place.
Answer:
247.3 Ft
Step-by-step explanation:
c=3.14(78.75)
c=247.245 *rounded*
The question was about calculating the circumference of a circle using its diameter. The diameter was given, and the formula for circumference 'C = πd' was used, where 'd' was 78.75 feet and 'π' was approximated at 3.14. The circumference comes out to be approximately 247.35 feet when rounded to the nearest tenth.
Explanation:The subject in this question is the measurement of the circumference of a cookie given its diameter, a basic concept in geometry in the field of Mathematics. Circumference which is the distance around a circle can be calculated using the formula 'C = πd', where 'C' is the circumference, 'd' is the diameter and 'π' is a constant approximately equal to 3.14.
In this case, the diameter 'd' of the cookie is 78.75 feet. So, by substituting the values into the formula, we get: C = 3.14 * 78.75.
After performing this calculation, you'll find that the approximate circumference of the cookie is 247.35 feet when rounded to the nearest tenth.
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A small accounting firm has 444 accountants who each earn a different salary between \$50{,}000$50,000dollar sign, 50, comma, 000 and \$60{,}000$60,000dollar sign, 60, comma, 000, and a 5^{\text{th}}5 th 5, start superscript, start text, t, h, end text, end superscript accountant who works part-time for tax season and earns \$10{,}000$10,000dollar sign, 10, comma, 000. [Show data] 1010 5252 5454 5656 5858 The firm decides to get rid of the part-time accountant and keep the other 444 salaries the same. How will getting rid of the part-time accountant affect the mean and median? Choose 1 answer: Choose 1 answer: (Choice A) A Both the mean and median will increase, but the median will increase by more than the mean. (Choice B) B Both the mean and median will increase, but the mean will increase by more than the median. (Choice C) C The mean will increase, and the median will decrease. (Choice D) D The median will increase, and the mean will decrease.
Answer:
The correct option is;
(Choice B) Both the mean and median will increase, but the mean will increase by more than the median.
Step-by-step explanation:
Here, we are expected to show the differences (advantages/properties) of the mean and median
Note that the definition of the mean is the sum of the value of all data points divided by the number of data points
Assuming the four accountants each earn $ 55,000.00
Therefore, initial mean before getting rd of the part-time accountant is
(55+ 55+ 55 + 55 + 10)/5 = 46
Final mean after the part-time accountant is gone =(55+ 55+ 55 + 55 )/4 = 55
Therefore the mean increases
However, the median is given by the middle value when the list of values are arranged in increasing order as
55, 55, 55, 55, 10
Therefore the initial median is 55
Final median after the part-time accountant is gone is
55, 55, 55, 55
Therefore, final = (55 + 55)/2 = 55
That is the median remains the same that is little or increase.
Therefore, since the range of values for the full time accountants salaries weigh less than the difference between the average full time salary and a single part time, both the mean and the median will increase but the mean will increase more than the median
Answer:
b
Step-by-step explanation:
suppose you have a 4-liter bucket and a 7-liter bucket. you need 5-liters for an aquarium. Explain how to get 5liters if neither bucket is marked?
Answer:
it is a 7 step process explained in explanation section
Step-by-step explanation:
Step one
fill 7 litre bucket then pour it in 4 liter bucket
output: 7 litre bucket has 3 litres and 4 litres bucket has 4 liter in it
Step two
drain four liter bucket and pour 3 liter from 7 litre bucket in it
output: 7 litre bucket has 0 litres and 4 litres bucket has 3 liter in it
step 3
fill 7 litre bucket and transfer water from it in 4 liter bucket which has already 3 liter in it
output: 7 litre bucket has 6 litres and 4 litres bucket has 4 liter in it
step 4
drain four liter bucket and pour 4 liter from 7 litre bucket which has 6 litre in it
output: 7 litre bucket has 2 litres and 4 litres bucket has 4 liter in it
step 5
drain 4 litre bucket and pour 2 litre from 7 litre bucket
output: 7 litre bucket has 0 litres and 4 litres bucket has 2 liter in it.
step 6
fill 7 liter bucket fully
output: 7 litre bucket has 7 litres and 4 litres bucket has 2 liter in it.
step 7
pour water from 7 liter bucket in 4 litre bucket which has already 2 litre in it
output: 7 litre bucket has 5 litres and 4 litres bucket has 4 liter in it.
A bonsai tree is 18 inches wide and stands 2 feet tall. What is the ration of the width of the bonsai to its height?
Answer:
3:4
Step-by-step explanation:
Before we start to deal with the ratio, we need all lengths in the same units.
The width is 18 inches.
The height is 2 feet.
Let's convert the height to inches. Then we will have both dimensions in the same units, inches.
2 ft * (12 in.)/ft = 24 in.
Now we have:
width = 18 in.
height = 24 in.
ratio of width to height = 18 in. to 24 in. = 18/24 = 3/4 = 3:4
The ratio of the width to the height of the bonsai tree is 3:4 after converting the height into inches and simplifying the ratio.
Explanation:The question asks to find the ratio of the width of a bonsai tree to its height. Since the width is given in inches and the height in feet, we first need to convert the height into inches to have a consistent unit of measure. There are 12 inches in 1 foot, so the bonsai tree's height is 2 feet times 12 inches/foot, which equals 24 inches.
Now, we can write the ratio of the width to height as 18 inches (width) to 24 inches (height). This simplifies to 3:4 after dividing both terms by the greatest common factor, which is 6.
Convert the angle \theta=\dfrac{17\pi}{18}θ= 18 17π theta, equals, start fraction, 17, pi, divided by, 18, end fraction radians to degrees. Express your answer exactly. \theta=θ=theta, equals ^\circ ∘
Answer:
θ = 170°
Step-by-step explanation:
Given angle is in radian as,
[tex]\theta^{c} = \dfrac{17 \pi}{18}[/tex]
Here, [tex]\theta^{c}[/tex] symbol represents the angle is in radian.
To convert given angle into degree, multiply the given angle with conversion factor as follows,
[tex]\theta^{\circ} = \theta^{c} \times \left(\frac{180}{\pi }\right)^{\circ}[/tex]
Substituting the values,
[tex]\theta^{\circ} = \dfrac{17 \pi}{18} \times \left(\dfrac{180}{\pi }\right)[/tex]
Cancelling out the common terms,
[tex]\theta^{\circ} =17\times \left(10\right)[/tex]
Therefore,
[tex]\theta^{\circ} =170^{\circ}[/tex]
Therefore the value of given angle in degree is 170°
To convert radians to degrees, utilize the conversion factor 180/π. In this instance, we have the angle (17π / 18) radians, which simplifies to 170 degrees when converted to the degree format.
Explanation:The subject topic of this conversation is about converting radians to degrees. Specifically, we're looking at how to convert the radian measurement = 17 / 18 into degrees.
One radian is equivalent to 180/ degrees. As such, to convert radians to degrees, you multiply the radian measurement by this conversion factor (180/).
Have a look at the calculation: = (17 / 18) * (180/).
The cancels out leaving us with / * . This calculation gives us = 170 degrees.
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The graph of the function f(x) = (x − 3)(x + 1) is shown. Which describes all of the values for which the graph is positive and decreasing?
all real values of x where x < −1
all real values of x where x < 1
all real values of x where 1 < x < 3
all real values of x where x > 3
Answer:
option a all real values of x where x < −1
Step-by-step explanation:
(6x2 + 4x +1) - (4x + 20)
Answer:
(6x² + 4x +1) - (4x + 20) = 6x² + 21
Step-by-step explanation:
(6x² + 4x +1) - (4x + 20)
= 6x² + 4x -4x + 1 + 20
= 6x² + 21
Factor this expression completely.
-21x + 28
7 (3x - 4)
-7(3x – 4)
- 7 (3x + 4)
- (21x - 4)
Answer:
− 21 x + 28 , 7 , 3 x − 4 , − 7 ( 3 x − 4 ) , − 7 , 3 x + 4 , − ( 21 x − 4 )
Step-by-step explanation:
too much to explain sorry
Hope this helped!
The factor of the expression -21x + 28 is equal to -7(3x – 4). The correct option is B.
What is an expression?The numerical variables and operations denoted by the addition, subtraction, multiplication, and division signs are combined in the mathematical expression.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols. They can also denote the operation order and other properties of the logical syntax.
Given expression is -21x + 28, The value of the expression will be calculated as,
E = -21x + 28
Take -7 common from the whole expression,
E = -21x + 28
E = -7 ( 3x - 4 )
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How do I simplify this.
Answer:
8/5
Step-by-step explanation:
I'd write the following:
2 1
---- ÷ ----
5 4
To divide by a fraction (such as 1/4), invert the divisor fraction and multiply instead:
2 4
---- · ---- = 8/5
5 1
In a right triangle, the value of cos B = 3/5. What is the value of sin B?
[Leave your answer as a fraction]
Answer:
4/5
Step-by-step explanation:
cos B = 3/5
cos Ф = adjacent/hypothesis
hypothesis ² = adjacent² + opposite²
5²= 3²+ o²
25 = 9+o²
25-9=o²
16 = o²
√16 = o = 4
Sin B = opposite/hypothesis = 4/5
What is the equation of the line that passes through the point (-5,3)(−5,3) and has a slope of fraction -6/5
Answer:
Step-by-step explanation:
Use the point-slope formula.
y - y_1 = m(x - x_1) when : x_1 = -5 and y_1 =3 and m= -6/5
the equation : y - 3 = -6/5(x +5)
Answer:
y=-6/5x-3
Step-by-step explanation:
Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics grow procedure that utilized water containing the nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after germination. Those heights, measured in millimeters, were as follows: 53.1, 60.2, 60.6, 62.1, 64.4, 68.6. Given a margin of error of 5.4 mm, construct a 95% confidence interval for the population mean height.
Answer: The required confidence interval is (56.1,66.9).
Step-by-step explanation:
Since we have given that
53.1, 60.2, 60.6, 62.1, 64.4, 68.6
[tex]\bar{x}=\dfrac{53.1+60.2+60.6+62.1+64.4+68.6}{6}=\dfrac{369}{6}=61.5[/tex]
n = 6
Margin of error = 5.4
At 95% level of confidence, z = 1.96
So, the confidence interval would be
[tex]\bar{x}\pm \text{Margin of error}\\\\=61.5\pm 5.4\\\\=(61.5-5.4,61.5+5.4)\\\\=(56.1,66.9)[/tex]
Hence, the required confidence interval is (56.1,66.9).
Which of the following statements are true about the string lengths for the first craft project and the new project?
Select all that apply.
A.
There are half as many 12-inch strings for the new project as for the craft project.
B.
There are twice as many 8-inch strings for the craft project as for the new project.
C.
Jasmine has the same number of strings for the new project as for the craft project.
D.
The total length of the strings for the craft project is greater than the total length for the new project.
E.
The length of the longest string is the same for both projects.
HELP
SOMEBODY!
the answers are c and d
Math Question Please Help! 25 pts!!!
1.) A basketball player made 2 out of 4 free throws she attempted which is 50%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by attempts or percent of successful free throws to 75%.
A) Write an equation to represent this situation.
B) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 75%?
Answer:
A) (2+x)/(4+x) × 100 = 75
B) 4
Step-by-step explanation:
2 out of 4
(2+x) out of (4+x)
(2+x)/(4+x) × 100 = 75
(2+x)/(4+x) = 3/4
8 + 4x = 12 + 3x
x = 4
d + 0.5 = 0.75
d =
Solve the equation.
Answer: 0.25
Step-by-step explanation:
0.75-0.5= 0.25
Answer:
d= 0.75-0.5
d= 0.25
Step-by-step explanation:
so firstly you subtract 0.5 from both sides
d= 0.75-0.5
d=0.25
What word goes with the image?
Answer:
Wavelength
Step-by-step explanation:
The picture below is an example of a wavelength which is very similar.
Step-by-step explanation:
FASST PLZZZ!! It’s really important!!!
Answer:
The second, third and fifth are true.
Step-by-step explanation:
1) False, the radius is d÷2=8÷2=4 cm
2) True, C = 2×π×r = π×d = 8π
3) True, C = 8π = 8 × 22/7 = 176÷6 ≈ 25,14
4) False, C = 25,14 ≈ 25
5) True, C = 8π = 8×3,14 = 25,12
Answer: B,C,E
Step-by-step explanation:
Find the angles in this quadilateral
Answer:
Therefore a= 90°,b=54°, x=54°, y= 162°
Step-by-step explanation:
a=90°
a:b=5:3
5+3= 8
5/8 x A = 90
A is the sum of the angles of a and b divided in the ratio 5:3
5A/8 = 90
cross multiply
5A= 90 X8 = 720
5A=720
A= 720/5= 144°
b= 3/8 x 144 = 3x144/8 = 432/8 = 54
a= 90
b= 54
x:y is in the ratio of 1:3
the Sum of angles in a Quadrilateral is 360°
if the sum of a and b is 144°
then the reamining angles is 360-144= 216°
then x:y=1:3
1+3=4
x= 1/4 x 216= 54°
y= 3/4 x 216= 162°
Therefore a= 90°,b=54°, x=54°, y= 162°
we can see that b = x = 54°
How much carbon dioxide is produced from running a microwave (1500 watts) for 10 minutes per day for one month? (round to the tenths place)
HINT: 1.37 pounds CO2 per kWh
Answer: 10.3 pounds of CO2 is produced
Step-by-step explanation:
Assuming there are 30 days in a month, if the microwave is run for 10 minutes per day, then the number of minutes for which the microwave is run in a month is
30 × 10 = 300 minutes
We would convert from minutes to hours
60 minutes = 1 hour
Therefore,
300 minutes = 300/60 = 5 hours
Also,
1000 watts = 1 kW
Therefore,
1500 watts = 1500/100 = 1.5kw
Therefore, the number of kWh is
1.5 × 5 = 7.5 kWh
If 1.37 pounds CO2 per kWh, then
If 1kWh = 1.37 pounds CO2, then
7.5 kWh = 7.5 × 1.37 = 10.3 pounds rounded to the nearest tenth
Final answer:
A 1500-watt microwave running for 10 minutes per day for one month emits approximately 10.3 pounds of CO2 when rounding to the tenths place.
Explanation:
The question is how much carbon dioxide is produced from running a 1500-watt microwave for 10 minutes a day for a month. To solve this, we first need to calculate the total energy used by the microwave in kWh. Since the microwave uses 1500 watts and is used for 10 minutes daily, we convert this to hours:
10 minutes = 10/60 hours = 1/6 hour
Power in kWh = Power in watts / 1000
Energy used per day in kWh = (1500 watts / 1000) x (1/6 hour) = 0.25 kWh
Next, we need to calculate the monthly energy use:
Energy used per month in kWh = 0.25 kWh/day x 30 days = 7.5 kWh
Using the given conversion factor of 1.37 pounds of CO2 per kWh, the total CO2 emissions can be calculated:
CO2 emissions = 7.5 kWh x 1.37 pounds CO2/kWh = 10.275 pounds of CO2
Finally, rounding to the tenths place:
CO2 emissions for the month = 10.3 pounds (rounded)
In your own words, describe what an exponential function is.
An exponential function is a mathematical concept characterized by a constant base elevated by a variable exponent. The rate of growth or decay of the function is proportional to its current value, leading to exponential growth or decay.
Explanation:An exponential function is a mathematical concept where a constant base is elevated by a variable exponent. The base could be any positive value different from one. A simple example of this type of function is f(x) = 2^x, where 2 is the constant base and x is the variable exponent.
The unique property of an exponential function is that the rate of growth or decay is proportionate to its current value. This means, as the variable x increases, the function value increases exponentially when the base is greater than one - thus showing exponential growth. Conversely, if the base is less than one but greater than zero, the function value decreases as x increases - thus representing exponential decay.
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Solve using quadratic formula
Show your work please!!!!
x^2 + 1/3x + 5/6 = 0
Answer:
0.3. and 2
Step-by-step explanation:
For this equation: a=1, b=0.3333333333333333, c=0.8333333333333334
1x2+0.333333x+0.833333=0
Step 1: Use quadratic formula with a=1, b=0.3333333333333333, c=0.8333333333333334.
x=
−b±√b2−4ac
2a
x=
−(0.333333)±√(0.333333)2−4(1)(0.833333)
2(1)
x=
−0.3333333333333333±√−3.222222
2
i think this is right :)
Could 1.5, 2.5, 3.5 and 6, 10, 12 be the corresponding sides of two similar triangles
Answer:
No
Step-by-step explanation:
If the ratios of the corresponding sides are equal then they would be the sides of 2 similar triangles.
Calculate the ratio of corresponding sides.
[tex]\frac{6}{1.5}[/tex] = 4
[tex]\frac{10}{2.5}[/tex] = 4
[tex]\frac{12}{3.5}[/tex] ≠ 4
Thus the sides are not the corresponding sides of similar triangles.