Answer:
a=15
Step-by-step explanation:
3a+b = 54
Let b=9
3a+9 = 54
Subtract 9 from each side
3a+9-9= 54-9
3a = 45
Divide each side by 3
3a/3 = 45/3
a = 15
Answer:
[tex]3a+b=54[/tex]
[tex]3a+9=54\:[b=9][/tex]
[tex]3a=54-9[/tex]
Subtract 9 from both sides
[tex]3a=45[/tex]
Divide both sides by 3
[tex]\frac{3a}{3}=\frac{45}{3}[/tex]
[tex]a=15[/tex]
OAmalOHopeO
Seventy of Myra’s classmates are traveling by bus to a football game in another town. They hired 2 buses, but there were only 64 seats. The remaining 6 students had to travel in a separate van.
The equation 2b + 6 = 70 represents the given scenario. What does b represent?
Answer:
seats in each bus
Step-by-step explanation:
total no.of seats = 64
so, the no.of seats in each bus = 64/2 =32
therefore , b denotes the no.of seats in each bus
PLEASE MARK ME AS BRAINLIEST .
shanika has a lamp that she wants to send to her sister in baltimore.the lamp is in the shape of a rectangular prism.it measures 14 high, 9 wide, and 3 long.she wants to buy a box so that there is 1 all around the lamp for bubble wrap
Consider we need to find the dimensions and volume of the box.
Given:
The shape of the lamp is a rectangular prism.
It measures 14 high, 9 wide, and 3 long.
There is 1 all around the lamp for bubble wrap
To find:
The dimensions and volume of the box.
Solution:
Length of the box is:
[tex]3+2=5[/tex]
Width of the box is:
[tex]9+2=11[/tex]
Height of the box is:
[tex]14+2=16[/tex]
Therefore, the dimensions of the box are 5 by 11 by 16 units.
The volume of the box is:
[tex]V=l\times w\times h[/tex]
Where, l is length, w is width and h is height.
Putting [tex]l=5, w=11, h=16[/tex], we get
[tex]V=5\times 11\times 16[/tex]
[tex]V=880[/tex]
Therefore, the volume of the box is 880 cubic units.
A record club has found that the marginal profit,
Upper P prime (x ), in cents, is given by
Upper P prime (x )equals negative 0.0008 x cubed plus 0.20 x squared plus 46.8 x for x less than or equals 200,
where x is the number of members currently enrolled in the club. Approximate the total profit when 120 members are enrolled by computing the sum
Summation from i equals 1 to 6 Upper P prime (x Subscript i Baseline )Upper Delta x with Upper Delta x equals 20.
Solution :
Given :
[tex]$P'(x) = -0.0008x^3+0.20x^2+46.8x,$[/tex] for x ≤ 200
Total profit when 120 members are enrolled is :
[tex]$\sum_{i=1}^6P'(x_i) \Delta x$[/tex] with [tex]\Delta x = 20[/tex]
Using the left end points, we get,
The values of [tex]x_i[/tex] are : { 0, 20, 40, 60, 80, 100}
Therefore,
[tex]$P'(x_1) = P'(0)=-(0.0008)(0)^3+(0.20)(0)^2+(46.8)(0)$[/tex]
= 0
[tex]$P'(x_2) = P'(20)=-(0.0008)(20)^3+(0.20)(20)^2+(46.8)(20)$[/tex]
= 1009.6
[tex]$P'(x_3) = P'(40)=-(0.0008)(40)^3+(0.20)(40)^2+(46.8)(40)$[/tex]
= 2140.8
[tex]$P'(x_4) = P'(60)=-(0.0008)(60)^3+(0.20)(60)^2+(46.8)(60)$[/tex]
= 3355.2
[tex]$P'(x_5) = P'(80)=-(0.0008)(80)^3+(0.20)(80)^2+(46.8)(80)$[/tex]
= 4614.4
[tex]$P'(x_6) = P'(100)=-(0.0008)(100)^3+(0.20)(100)^2+(46.8)(100)$[/tex]
= 5880
[tex]$\sum_{i=1}^6P'(x_i) \Delta x = P'(x_1)\Delta x + P'(x_2)\Delta x + P'(x_3)\Delta x + P'(x_4)\Delta x + P'(x_5)\Delta x + P'(x_6)\Delta x $[/tex]
= (0)(20) + (1009.6)(20) + (2140.8)(20) + (3355.2)(20) + (4614.4)(20) + (5880)(20)
= (20)( 0 + 1009.6 + 2140.8 + 3355.2 + 4614.4 + 5880)
= (20)(17,000)
= 340,000 cents
[tex]$=\frac{340000}{100} \ \text{dollars}$[/tex]
= 3400 dollars
Hence, the required total profit is 3400 dollars.
Someone help me pls ..
Answer:
because they are both in the circle
Step-by-step explanation:
An amusement park charges and admission fee of 30 dollars for each person. Let C be the cost (in dollars) of admission for P people. Write an equation relating C to P.
Answer:
14
Step-by-step explanation: B is the midpoint of AC, in other words it is the halfway point.
So A to B should be equal to B to C
Our expression is:
2x + 9 = 37
Subtract 9
2x = 28
Divide by 2
x = 14
Sophia pays £222 for a plane ticket.
She also pays 100 euros airport tax.
The exchange rate is £1 = 1.38 euros.
What percentage of the total cost of the ticket and the airport tax does Sophia pay
for the
airport tax?
Give your answer correct to 1 decimal place.
9514 1404 393
Answer:
24.6%
Step-by-step explanation:
The cost of the ticket in euros is ...
£222 × €1.38/(£1) = €306.36
Then the ratio of the tax to the to the total cost is ...
€100/(€306.36 +100) = 100/406.36 ≈ 24.6%
Determining if a Relationship Is a Function
Which represents a function?
Answer:
only the first one...
a "FUNCTION" has a UNIQUE relation between each input and output...
notice the middle one the -2 goes to BOTH th2 10 & -7 that makes it NOT a FUNCTION
Step-by-step explanation:
whats the perimeter and area of this shape?
Answer:
The perimeter 9+9+15+4+3+4pi=52.56 units.
The area is 25.12+135 which is 160.12 unit squared.
Step-by-step explanation:
Perimeter of this shape = perimeter of half circle + perimeter of the rectangle
Diameter of circle = 15-4-3 = 8
Radius of circle = 8/2 = 4
Perimeter of the shape = (2 x pi x 4)/2 + 15 + 9 + 9 + 4 + 3
= 4pi + 40 = 52.56 units (substitute pi = 3.14)
Area of shape = area of half circle + area of rectangle
= (pi x 4 x 4)/2 + (9 x 15)
= 25.12 + 135 = 160.12 unit squared
Select the correct answer.
Function h is a transformation of the parent exponential function, f(x) = 2^x.
.h(x)=-3.2^x
-
Which statement is true?
Find the measure of each angle indicated.
890
50°
A) 44°
C) 47°
B) 51°
D) 71°
Answer:
51
Step-by-step explanation:
See the other answer
Answer:
(B). 51°
Step-by-step explanation:
A certain forest covers an area of 2300 km. Suppose that each area decreases by 5.75%. What will be the area after 12 years?
Answer:
The correct answer is 2043 km².
Step-by-step explanation:
Given:
Starting area,
A = 2300 km²
Rate of decreasing,
r = 5.75%
Time,
t = 12 years
As we know,
⇒ [tex]y = A(1-r)^t[/tex]
By substituting the values, we get
[tex]=2300(1-0.0575 )^{12}[/tex]
[tex]=2300(0.9425)^{12}[/tex]
[tex]=2300\times 0.8883[/tex]
[tex]=2043 \ km^2[/tex]
Taylor has nickels and dimes. The number of nickels is 7 less then eight times the number of dimes. If d represents the number of dimes then the number of nickels can be expressed as what
Answer: [tex]8d-7[/tex]
Step-by-step explanation:
Given
Taylor has nickels and dimes
Number of nickels is 7 less than eight times the number of dimes
If d is the number of dimes, then number of nickels is given by
[tex]\Rightarrow \text{Number of Nickels = }8d-7[/tex]
Given the function F (x) 2/3 x -5 , evaluate f(9)
A polling organization surveyed 2,000 residents of a town for their views on the mayor, and 1,640 respondents said they approved of the mayor. The organization then published a report of its findings, stating a range of the percentages of residents who approve of the mayor with 95% confidence. Based on this information, what is the lowest possible percentage of residents who approve of the mayor?
Answer:
80.32%
Step-by-step explanation:
The proportion who approved of the mayor :
p = number who approved of the mayor / total respondents = 1640 / 2000 = 0.82
The confidence interval for proportion is given by :
p ± Zcritical * √p(1 - p) / n
Zcritical at 95% = 1.96 (Z standard table distribution)
0.82 ± 1.96 * √0.82(0.18) / 2000
0.82 ± 1.96 * 0.0085906
0.82 ± 0.0168377
(0.8032 ; 0.8368)
Lower boundary = 0.8032
Answer:
See image below
Step-by-step explanation:
How to find the exact answer of the area and circumference
I know how to find the approximate answer for both but i don’t know how to find the exact answer. Pi should be included in the exact fraction.
Can someone explain pls:)
Answer:
[tex]\pi \\[/tex] is irrational so any attempt to use 3.14... is never EXACT...
do not try to convert it ... if it asks for exact..
write 81[tex]\pi \\[/tex] or 9 [tex]\pi \\[/tex] etc. don't put in 63.62 like answers
Step-by-step explanation:
I’m stuck on this one help anyone?
Answer:
just add a small amount to the 2.8 and square the result
Step-by-step explanation:
x x^2
2.8 7.84
2.81 7.8961
2.82 7.9524
2.83 8.0089
2.84 8.0656
2.85 8.1225
2.86 8.1796
2.87 8.2369
How much money invested at 3% compounded monthly for 3 years will yield $520?
$179.42
$475.30
$358.84
$148.78
Answer:
Step-by-step explanation:
Use this formula:
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex] where A(t) is the amount after the compounding is done, P is the initial investment (our unknown), r is the interest rate in decimal form, n is the number of compoundings per year, and t is the time in years. Filling in:
[tex]520=P(1+\frac{.03}{12})^{(12)(3)}[/tex] and simplifying that a bit:
[tex]520=P(1+.0025)^{36[/tex] and a bit more:
[tex]520=P(1.0025)^{36[/tex] and even bit more:
520 = P(1.094551401) and divide to get
P = $475.30
what is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.
a. 0.02
b. 0.14
c.0.34
d.0.84
You want to find Pr[-2 < Z < -1].
The table tells you that
• Pr[Z < 0] = 0.5000
• Pr[Z < 1.00] = 0.8412
• Pr[Z < 2.00] = 0.9772
• Pr[Z < 3.00] = 0.9987
We have
Pr[-2 < Z < -1] = Pr[Z < -1] - Pr[Z < -2]
(because the distribution of Z is continuous)
… = Pr[Z > 1] - Pr[Z > 2]
(by symmetry of the distribution about its mean)
… = (1 - Pr[Z < 1]) - (1 - Pr[Z < 2])
(by definition of complement)
… = Pr[Z < 2] - Pr[Z < 1]
… = 0.9772 - 0.8412
… = 0.1360 ≈ 0.14 … … … (B)
Answer:
it's B aka 0.10.14
Step-by-step explanation:
Find the value of x.
B
X+2
3
D
E
х
2
А
x = [?]
Answer:
x = 4
Step-by-step explanation:
The line DE is parallel to AC and divides the sides proportionally, that is
[tex]\frac{BD}{AD}[/tex] = [tex]\frac{BE}{CE}[/tex] , substitute values
[tex]\frac{x+2}{x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
3x = 2(x + 2) = 2x + 4 ( subtract 2x from both sides )
x = 4
Find the volume of a cone with a base radius of 4 ft and a height of 6 ft. I really need help with this asap. I will give 10 points to whoever can solve it...
Step-by-step explanation:
V=1/3 × πr²h
since H=6, R=4
V= π×(4)²×(6)/3
V=96π/3
V=32π
Note: ( we are not given the pie (π) value )
Answer:
Step-by-step explanation:
r = 4
h = 6
pi = 3.14
Formula
V = 1/3 pi r^2 h
V = 1/3 3.14 * 4^2 * 6
V = 1/3 * 3.14 * 16 * 6
V = 100.48
Which of the following equations would not have a solution that is the same as the solution to the system. shown below?
4x+y=7
-2x+5y=1
———————————————
1) 11y = 9
2) 2x + 6y = 8
3) -4x + 10y = 1
4) 12x + 3y = 21
please help asap and thank you in advance to anyone who answers this for me ! :)
Answer:
Step-by-step explanation:
Can someone help me please
Answer:
ok
Step-by-step explanation:
Two legs of a right triangle measure 23 inches and 38 inches. What is the length of the hypotenuse, to the nearest
inch?
Answer:
hypotenuse ≈ 44 inches
Step-by-step explanation:
Using Pythagoras' identity
The square on the hypotenuse is equal to the sum of the squares on the other two sides.
let the hypotenuse be h , then
h² = 23² + 38² = 529 + 1444 = 1973 ( take square root of both sides )
h = [tex]\sqrt{1973}[/tex] ≈ 44 inches ( to the nearest inch )
what is the approximate circumference of the circle shown below?
Answer:
B. 56.52
Step-by-step explanation:
C = 2πr
C = circumferencer = radius of the circlethe constant pi = 3.14Therefore,
56.52 = 2(3.14)(9)
Feel free to message me if you still have questions :)
Examine circle O, where chords AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ are congruent.
Point P lies on AB¯¯¯¯¯¯¯¯ and point Q lies on CD¯¯¯¯¯¯¯¯.
Angles APO and DQO are right angles.
The diagram as described in the problem.
Which congruence statement is true?
CD≅AP
QD≅QO
OP≅OQ
OP≅AB
what’s the answer to this ?
Answer:
|||
Step-by-step explanation:
the answer is c (|||)
Answer:
the answer is c
Step-by-step explanation:
the answer is C(111)
Find the value of x for the right triangle.
b2 is A= 1/2h(bl+b2), if A=16, h=4, and b1=3
b2=____
Answer:
b₂ = 5
Step-by-step explanation:
Substitute the given values into the formula
16 = [tex]\frac{1}{2}[/tex] × 4 × (3 + b₂)
16 = 2(3 + b₂) ( divide both sides by 2 )
8 = 3 + b₂ ( subtract 3 from both sides )
5 = b₂
SOMEONEEEE PLEASEEEEE HELPPPPP MEEEEE OUTTTTT!!!! ASAPPP
Answer:
3/4
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan X = opp side / adj side
tan X = 24/32
tan X = 3/4
Answer:
tan X = 24/32
Step-by-step explanation:
Using SOH-CAH-TOA, we can figure out tan X.
To find tan. the equation is opposite over adjacent.
So, tan X = 24/32.
Mr Lorenzo must make a minimum of 48 circuit boards per day. On Wednesday he made 60. What percent of required minimum did he make
Answer:
He made 125% of the required minimum.
Step-by-step explanation:
Percentage:
The percentage that a number b is of a is given by:
[tex]P = \frac{100b}{a}[/tex]
In this question:
Minimum of 48, made 60. The percentage 60 is of 48 is:
[tex]P = \frac{100(60)}{(48)} = 100(1.25) = 125[/tex]
He made 125% of the required minimum.
