The value of h(t) when [tex]t=\frac{15}{32}[/tex] is 10.02.
Solution:
Given function [tex]h(t)=-16t^2+15t+6.5[/tex]
To find the value of h(t) when [tex]t=\frac{15}{32}[/tex]:
[tex]h(t)=-16t^2+15t+6.5[/tex]
Substitute [tex]t=\frac{15}{32}[/tex] in the given function.
[tex]$h\left(\frac{15}{32} \right)=-16\left(\frac{15}{32} \right)^2+15\left(\frac{15}{32} \right)+6.5[/tex]
[tex]$=-16\left(\frac{225}{1024} \right)+15\left(\frac{15}{32} \right)+6.5[/tex]
Now multiply the common terms into inside the bracket.
[tex]$=-\left(\frac{3600}{1024} \right)+\left(\frac{225}{32} \right)+6.5[/tex]
Now, in the first term, the numerator and denominator both have common factor 16. So reduce the first term into the lowest term.
[tex]$=-\left(\frac{225}{64} \right)+\left(\frac{225}{32} \right)+6.5[/tex]
To make the denominator same, take LCM of the denominators.
LCM of 64 and 32 = 64
[tex]$=-\left(\frac{225}{64} \right)+\left(\frac{225\times2}{32\times2} \right)+6.5\times\frac{64}{64}[/tex]
[tex]$=-\frac{225}{64} +\frac{450}{64}+\frac{416}{64}[/tex]
[tex]$=\frac{-225+450+416}{64}[/tex]
[tex]$=\frac{641}{64}[/tex]
= 10.02
[tex]$h\left(\frac{15}{32} \right)=10.02[/tex]
Hence the value of h(t) when [tex]t=\frac{15}{32}[/tex] is 10.02.
What is the median for 5, 5, 5, 10, 10, 15, 15, 20, 25, 30, 35, 40, 40, 45, 50, 50?
Answer:
22.5
Step-by-step explanation:
1) Arrange the numbers in order by size.
(5,5,5,10,10,15,15,20,25,30,35,40,40,45,50,50)
2) If there is an odd number of terms, the median is the center term.
3) If there is an even number of terms, add the two middle terms and divide by 2.
(25+20=45)
45 divided by 2 is 22.5
22.5 is your median
A shopper buys cat food in bags 4 lbs. her cat eats 3/4 lb each week. How many weeks does one bag last? Draw a diagram
Answer:
5 weeks
Step-by-step explanation:
Finding the Median from a Dot Plot
Highlands
The dot plots show rainfall totals for several spring
in highland areas and lowland areas.
What is the median rainfall for the highland storms?
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Rainfall (mm)
Lowlands
median rainfall for the lowland storms?
LLLLLLL
2
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Rainfall (mm)
Answer:
16mm and 12mm
Step-by-step explanation:
Final answer:
The median rainfall for the highland storms is 19 mm and for the lowland storms is 13 mm.
Explanation:
To find the median rainfall for the highland storms, we need to locate the middle value in the dot plot. Since there are 14 observations, the median is between the seventh value, 18, and the eighth value, 20. To find the median, add the two values together and divide by two: (18 + 20) / 2 = 19.
To find the median rainfall for the lowland storms, we also need to locate the middle value in the dot plot. Since there are 14 observations, the median is between the seventh value, 12, and the eighth value, 14. To find the median, add the two values together and divide by two: (12 + 14) / 2 = 13.
a collection of dimes an nickels is worth $3.30. if there are 42 coins in all, how many of each kind of coin is there ?
==============================
Work Shown:
d = number of dimes
n = number of nickels
10d = value of all the dimes in cents
5n = value of all the nickels in cents
10d+5n = total value of all the coins in cents
$3.30 = 3.30*100 = 330 cents
so one equation is 10d+5n = 330
-------
Let's set up the second equation
we have 42 coins, so n+d = 42
subtract d from both sides to get n = 42-d
-------
Go back to the first equation and apply substitution to solve for d.
10d+5n = 330
10d+5(42-d) = 330 ... plug in n = 42-d
10d+5(42)+5(-d) = 330 ... distribute
10d+210-5d = 330
5d+210 = 330
5d = 330-210 ... subtract 210 from both sides
5d = 120
d = 120/5 ... divide both sides by 5
d = 24
-------
Now we can use that to find n.
n = 42-d
n = 42-24 ... plug in d = 24
n = 18
------
Check:
n = 18 nickels
5*n = 5*18 = 90 cents from just the nickels
d = 24 dimes
10*d = 10*24 = 240 cents from just the dimes
5n+10d = 90+240 = 330 cents = $3.30 total from all the coins
n+d = 18+24 = 42 coins total
Answers are confirmed
Final answer:
To solve the question, set up a system of linear equations based on 0.10d + 0.05n = 3.30 and d + n = 42. Solve the system to find there are 33 dimes and 9 nickels in the collection.
Explanation:
The question involves solving a system of linear equations based on the given conditions involving dimes and nickels. To find out how many of each kind of coin there are, we can set up the following equations using the facts provided:
Let d be the number of dimes.
Let n be the number of nickels.
Since the total value is $3.30, we can write the equation: 0.10d + 0.05n = 3.30 (since a dime is worth 10 cents and a nickel is worth 5 cents).
We are also told that there are 42 coins in total, which gives us the equation: d + n = 42.
Now we have a system of equations:
0.10d + 0.05n = 3.30
d + n = 42
To solve this system, we can multiply the second equation by 0.10 to make the coefficient of d the same in both equations:
0.10d + 0.05n = 3.30
0.10d + 0.10n = 4.20
We then subtract the first equation from the second to eliminate d:
0.10n = 0.90
n = 9 nickels
Plugging n = 9 into the second original equation d + 9 = 42, we get:
d = 42 - 9
d = 33 dimes
Therefore, there are 33 dimes and 9 nickels in the collection.
Solve the following system of equations. What is the x-value of the solution?
3x + 2y = 7
x - y + 1 = 0
Answer:
x = 1
Step-by-step explanation:
Step 1: Choose one of the equations to solve for y:
x - y + 1 = 0
(-y) / -1 = (-1 - x) / -1
y = 1 + x
Step 2: Plug in y into either equation
3x + 2(1 + x) = 7
3x + 2 + 2x - 2= 7 - 2
5x / 5 = 5 / 5
x = 1
Answer: x = 1
kevin uses each of the digits 6,4,3 and 8, once and once only to make four digit numbers.
what is the smallest odd number that he can make?
Answer:
3468
Step-by-step explanation:
We can make four digit number from the digits 6,4,3,8
Smallest digit for thousands is 3=3000
Smallest digit for hundreds (out of remaining 6,4,8) is 4 = 400
Smallest digit for tenths (out of remaining 6,8) is 6= 60
And unit digit is 8
So the smallest number is 3000+400+60+8=3468 answer
There were 6 purple socks and 4 orange socks in a drawer. Zucky picked one sock without looking and then another without looking (or replacing the first). What is the probability that he picked 2 purple socks?
Answer: 1/3
Step-by-step explanation:
A customer at the grocery store purchased 27 apples and an unknown number of bananas. The customer purchased a total of 58 apples and bananas. Write an equation with a variable that represents this situation. Explain your process for determining this equation, then solve for how many bananas the customer purchased.
Answer:
The equation is
(x+27)= 58
Therefore the customer purchased 31 bananas
Step-by-step explanation:
Given , A customer at the grocery store purchased 27 apple and unknown number of bananas. The customer purchased a total of 58 apple and bananas.
Let the number bananas be x
He purchased a total (x+27) apples and bananas.
According to the problem,
(x+27)= 58
⇔x= 58-27
⇔x = 31
Therefore the customer purchased 31 bananas
Enter the value for x that makes the equation true
36(x-5)=9x-18
Answer:
x = 6
Step-by-step explanation:
Solve for x:
36 (x - 5) = 9 x - 18
Expand out terms of the left hand side:
36 x - 180 = 9 x - 18
Subtract 9 x from both sides:
(36 x - 9 x) - 180 = (9 x - 9 x) - 18
36 x - 9 x = 27 x:
27 x - 180 = (9 x - 9 x) - 18
9 x - 9 x = 0:
27 x - 180 = -18
Add 180 to both sides:
27 x + (180 - 180) = 180 - 18
180 - 180 = 0:
27 x = 180 - 18
180 - 18 = 162:
27 x = 162
Divide both sides of 27 x = 162 by 27:
(27 x)/27 = 162/27
27/27 = 1:
x = 162/27
The gcd of 162 and 27 is 27, so 162/27 = (27×6)/(27×1) = 27/27×6 = 6:
Answer: x = 6
The sum of 21, 1.7,0.25
21+1.7+0.25=22.95
You add 21+1.7, which equals 22.7, then add 0.25 to get 22.95.
The perimeter of a rectangular atrium is 104 inches. The length of the atrium is three times the width. Find the length and the width.
Answer:
Length = 39 inches , breadth = 13 inches
Step-by-step explanation:
Given:
The perimeter of a rectangular atrium is 104 inches.
The length of the atrium is three times the width.
Question asked:
The length and the breadth of rectangular atrium = ?
Solution:
Let breadth of rectangular atrium = [tex]x[/tex]
Then, the length of rectangular atrium = [tex]3x[/tex] (given)
Perimeter of rectangle = [tex]2\times(length + breadth)[/tex]
[tex]104 = 2\times( 3x + x )[/tex]
[tex]104 = 2\times 4x[/tex]
[tex]104 = 8x[/tex]
Dividing both side by 8
[tex]13 = x[/tex]
breadth of rectangular atrium = [tex]x[/tex] = 13 inches
length of rectangular atrium = [tex]3x[/tex] = [tex]3 \times13 = 39[/tex] inches
Thus, length and the breadth of rectangular atrium are 39 and 13 inches.
whats is 38.96×15.7
Ann thought of a number N, multiplied it by 5 and added 7. Then she told the result R to Jim. Write a formula that will tell you the value of R for any value of N
Answer:
[tex]R=5N +7[/tex]
Step-by-step explanation:
We want to write a formula for the statement:
Ann thought of a number N, multiplied it by 5 and added 7.
When we multiply N by 5, we get 5N
When we add 7 to 5N we get 5N+7
Our formula now becomes:
R=5N +7
The graph shows a vertical translation of y = RootIndex 3 StartRoot x EndRoot.
On a coordinate plane, a cube root function goes through (negative 4, negative 4), has an inflection point at (0, negative 2.5), and goes through (4, negative 1).
What is the range of the translated function?
{y|y < 0}
{y|y ≥ 0}
{y|y is a natural number}
{y|y is a real number}
{y|y is a real number}
The range of the translated function is {[tex]y|y[/tex] is a natural number}.
What is a real number and example?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5), and irrational numbers such as √3, π(22/7), etc., are all real numbers.
What is not a real number?The numbers which are not real and are Imaginary are known as not real or non-real numbers. Non-real numbers cannot be represented on the number line. Some of the types or examples of the non-real numbers are √−2,6√−54.
What makes a real number?The real number, in mathematics, is a quantity that can be expressed as an infinite decimal expansion. Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting.
Learn more about real numbers here: https://brainly.com/question/1770447
#SPJ2
Wskaż sumę liczb 2,5*10^10 i 7,8*10^10
odpowiedzi są takie:
A. 1,03*10^9
B. 1,03*10^10
C. 1,03*10^11
D. 10,3 * 10^20
proszę o pilną odpowiedź
To sum the numbers in scientific notation, you add the coefficients and keep the exponent. The correct sum of 2.5 \(\times\) 10^10 and 7.8 \(\times\) 10^10, expressed in proper scientific notation, is 1.03 \(\times\) 10^11.
Explanation:To find the sum of 2.5 \(\times\) 10^10 and 7.8 \(\times\) 10^10, you add the two numbers while keeping the same exponent since they are like terms in scientific notation. You calculate 2.5 + 7.8 which equals 10.3. Therefore, the sum in scientific notation is 10.3 \(\times\) 10^10.
However, in proper scientific notation, this number should have only one non-zero digit to the left of the decimal point. So, we adjust this sum by writing it as 1.03 \(\times\) 10^11 by moving the decimal one place to the left and increasing the exponent by 1. Thus, the correct answer is 1.03 \(\times\) 10^11, which correlates with option C.
Learn more about Adding Scientific Notation here:
https://brainly.com/question/31621311
#SPJ2
Jose bought a wallet for $19.95 and y hats for $5.99 each. Which of the following expressions shows the total amount of money he spent? (4 points)
Group of answer choices
19.95y + 5.99
19.95 + 5.99y
19.95 + 5.99 + y
19.95y + 5.99y
Answer:
Step-by-step explanation:
so he bought a wallet for 19.95 and y hats for 5.99
y = number of hats
19.95 + 5.99y....because each hat is 5.99
Divide. −5 5/6÷(−2 1/6)
Step-by-step explanation:
-5 5/6 ÷(-2 1/6)
Turn them into improper fractions
-35/6 and -13/6
Change the division sign to multiply
-35/6 × -13/6
Making -13/6 into -6/13
Solve
-35/6 × -6/13 = 210/78
Simplify
Answer:
35/13
Edit: if you want it to be a mixed number, it will be 2 9/13
Answer:
-5 5/6 ÷(-2 1/6)
Turn them into improper fractions
-35/6 and -13/6
Change the division sign to multiply
-35/6 × -13/6
Making -13/6 into -6/13
Solve
-35/6 × -6/13 = 210/78
Simplify explanation:
Solve the system of linear equations by substitution.What is the solution to x=2y+y and 3x+2y=3
Answer: the first one is 3y
Step-by-step explanation:
Go to the website mathpapa , type in the problem and it gives you the answer with steps
I need help please and thank you
Answer:
20 degrees.
Step-by-step explanation:
The 3 angles of a triangle add up to 180 degrees.
Therefore the third angle in this triangle
= 180 - (120 + 40)
= 180 - 160
= 20 degrees.
A company produces alarm clocks. During the regular workweek, the labor cost for producing one clock is $4.00
Answer:
The question is not complete, nut here is the complete question ; A company produces alarm clocks. During the regular workweek, the labor cost for producing one clock is $4.00. However, if a clock is produced on overtime, the labor cost is $5.00. Management has decided to spend no more than a total of $51,000 per week for labor. The company must produce 12,000 clocks this week. What is the minimum number of clocks that must be produced during the regular workweek?
Step-by-step explanation:
Tthe detailed analysis and step by step calculation is as shown in the attached file.
how do i find the imaginary unit?
[tex]\bf \pm\sqrt{-14}\implies \pm\sqrt{(-1)(14)}\implies \pm\sqrt{-1}\cdot \sqrt{14}\implies \stackrel{\sqrt{-1}}{\pm\stackrel{\downarrow }{i}\sqrt{14}}[/tex]
what is the soulution to the system
(-9,-9)
(-36,-9)
(-9,-36)
(9,-9)
Answer:
(-9,-9)
I Agree
Step-by-step explanation:
Which expression could be used to find the volume of the prism shown below?
A rectangular prism with length of 12, height of 10, and width of 4.
(4 times 12) times 10
(4 + 12) times 10
(10 + 4) times 12
(10 + 12) times 4
Answer:
The answer is A
Step-by-step explanation:
The volume is found by [tex]l*w*h[/tex]
Therefore you multiply, 4*12*10
Answer:
The answer is A
Step-by-step explanation:
Albert is five years younger than his brother bill. Write an equation that shows Albert's age with respect to Bills.
Answer:
A=B-5
Step-by-step explanation:
Albert is known as the variable A.
Bill is known as the variable B.
If Albert is 5 years younger than Bill. Then the equation will be
a=b-5
How do u do this with a guess check revise graph?
Answer:
12 inches by 15 inches
Step-by-step explanation:
Let
Width of the painting = x inches, then
Length of the painting [tex]=1\dfrac{1}{4}x[/tex] inches
The area of the painting:
[tex]A=\\ \\=\text{Width}\times \text{Length}=\\ \\=x\times 1\dfrac{1}{4}x=\\ \\=\dfrac{5}{4}x^2\ in^2[/tex]
Hence,
[tex]\dfrac{5}{4}x^2=180\\ \\x^2=\dfrac{4}{5}\times 180=4\times 36=144\\ \\x=12\ inches\\ \\\text{Width}=12\ inches\\ \\\text{Length}=\dfrac{5}{4}\times 12=15\ inches[/tex]
PLEASE HELP!!!!!! I really need help fast
Answer:
c
Step-by-step explanation:
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
Considering the small triangle in which the one side and two angles are given:
Finding the third angle of the small triangle
Sum of angles of the triangle is [tex]180[/tex]°
as two angles are given i.e 90° and 45°, so third angle is 180°-(90°+45°)
Third angle in the small triangle is 45°.
As the opposite angles are 45° joining together to form 90° angle, therefore the small triangle is an isosceles triangle in which the opposite sides are equal.
Therefore the two sides are 7 and 7 of small triangle, so By Pythagoras theorem the third side is
[tex]H=\sqrt{P^2+B^2}\\ \\=\sqrt{7^2+7^2}\\\\=\sqrt{98} \\H=7\sqrt{2}[/tex]
Similarly the bigger triangle is also an isosceles triangle whose base is determined i.e [tex]7\sqrt{2}[/tex] = perpendicular length of bigger triangle.
Applying the Pythagoras theorem in bigger triangle:
[tex]x=\sqrt{(7\sqrt{2})^2+(7\sqrt{2})^2 }\\x=\sqrt{98+98}\\\\ x=\sqrt{196} \\\\x=14[/tex]
Mr.Jenkins won $500 in a raffle. He split some of the money with his three children and had $20 left. How much money did he give each of his children?
Answer:460
Step-by-step explanation:
–72 = –10u + –22 what is u
Answer:
u = 5
Step-by-step explanation:
Kwasi reads 30 minutes before school. He reads x more minutes after school. Write an equation to represent the total number of minutes y Kwasi reads
One leg of a right triangle has a length of 3. The other sides have lengths that are consecutive integers. Find these lengths.
Answer:
Therefore other two sides of the triangle are 4 and 5.
Step-by-step explanation:
Given one leg of a right triangle has a length of 3
Let other sides of the triangle be x and x+1 [ since they are consecutive]
According to the problem,
3²+x²=(x+1)²
⇔9 + x²=x²+2x+1
⇔2x+1=9
⇔2x=9-1
⇔2x=8
⇔x=4
Therefore other two sides of the triangle are 4 and 5.
To find the lengths of the other two sides of the right triangle with one leg of length 3, we can use the Pythagorean theorem. The lengths of the other two sides are 4 and 5.
Explanation:To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Since one leg has a length of 3, let's call the lengths of the other two sides x and x+1. We can set up the equation:
3^2 + x^2 = (x+1)^2
Simplifying the equation:
9 + x^2 = x^2 + 2x + 1
Subtracting x^2 from both sides:
9 = 2x + 1
Subtracting 1 from both sides:
8 = 2x
Dividing both sides by 2:
4 = x
So, the lengths of the other two sides are 4 and 5.
Learn more about Pythagorean theorem here:https://brainly.com/question/19649203
#SPJ3