Answer:
44
Step-by-step explanation:
1×5² + 3×5¹ +4×5⁰
25+15+4
44
Casey's phone service charges a flat monthly fee of $30 for the first 1000 minutes of calls and $0.40 per minute over 1000. Determine Casey's monthly charge if he makes 1,100 minutes of calls?
Answer:
Casey's monthly charge for making 1,100 minutes of calls is $70.
Step-by-step explanation:
We can write a piecewise function to model the situation.
Since Casey's phone service only charges a monthly fee of $30 for the first 1000 minutes, we can write that for calling t minutes:
[tex]\displaystyle C(t) = 30\text{ if } t\leq 1000[/tex]
In other words, the total cost is only $30 is the total minutes of call is less than 1000 minutes.
However, if the total minutes of calls is greater than 1000, then its $0.40 per minute on top of the 30. Thus:
[tex]\displaystyle C(t) = 30 + 0.4(t-1000)\text{ if } t>1000[/tex]
All together, our piecewise function will be:
[tex]\displaystyle C(t) = \begin{cases} 30 & t\leq 1000 \\ 30 + 0.4(t-1000) & t>1000\end{cases}[/tex]
We want to determine Caseys monthly charge if he makes 1,100 minutes of calls. So, t = 1100. Since 1100 > 1000, we will use the second equation. This yields:
[tex]C(1100)= 30+0.4((1100)-1000)[/tex]
Evaluate:
[tex]\displaystyle C(1100) = 30+0.4(100) = 30+40=\$70[/tex]
Casey's monthly charge for using 1,100 minutes of call is $70.
A ball inside of a cube has a volume of 113 cubic inches. If each side of the cube measures 12.6 inches, what is the volume of air inside the cube? (Round to the nearest tenth.)
1357.1 cubic inches
1244.1 cubic inches
1887.4 cubic inches
1226.0 cubic inches
The volume of air inside the cube is 1887.4 cubic inches. Then the correct option is C.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A ball inside of a cube has a volume of 113 cubic inches. If each side of the cube measures 12.6 inches.
Then the volume of air inside the cube will be given as the difference between the volume of the cube and the sphere.
Air volume = Volume of the cube - Volume of the sphere
Air volume = 12.6³ - 113
Air volume = 2000.376 - 113
Air volume = 1887.376
Air volume ≅ 1,887.4
More about the geometry link is given below.
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Answer:
1887.4 cubic inches
Step-by-step explanation:
Need answers here! Tyy :)
Answer: The answer is 125 degree(third option)
Step-by-step explanation:
x + 55 = 180 {being co interior angles}
or, x = 180 - 55
so, x = 125
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. The article "Properties of Waste Silk Shod Fiber/Cellulose Green Composite Films" (. of Composite Materials, 2012: 123-127) reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.3 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value?
Complete Question
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.1 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.)
t=8.169
P-value= ?
Answer:
a) [tex]P-value=0[/tex]
b) Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=10[/tex]
Mean [tex]\=x= 51.3[/tex]
Standard deviation [tex]\sigma=1.2[/tex]
Significance level is taken as [tex]\alpha=0.05[/tex]
t test statistics
[tex]t=8.169[/tex]
Therefore
[tex]P-Value=P(t>8.169)[/tex]
Critical point
[tex]t_{\alpha,df}[/tex]
[tex]\alpha=0.05[/tex]
[tex]df=10-1=>9[/tex]
Therefore
P-value from T distribution table
[tex]P-value=0[/tex]
Conclusion
[tex]P-value (0)< \alpha(0.05)[/tex]
We Reject the Null Hypothesis [tex]H_0[/tex]
Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.
The graph of a linear function is given below. What is the zero of the function?
Answer:
Need to see the problem, but the "zero of the function" is the x value when y=0.
Substitute '0' for y.
Solve for x
Answer: D
Step-by-step explanation:
Corresponding sides of what triangles are proportional
Answer:
In a pair of similar triangles, the corresponding sides are proportional.
Step-by-step explanation:
Corresponding sides touch the same two angle pairs. When the sides are corresponding it means to go from one triangle to another you can multiply each side by the same number.
A gardener makes a new circular flower bed. The bed is ten feet in diameter.Calculate the circumference and the area of the circular flower bed
Answer:
It will be 31.4 cm rounded off for circumference
It will be 78.53 cm2 rounded off for area
Step-by-step explanation:
Diameter = 10 cm
Radius = 10/2 cm = 5 cm
Circumference = 2×pi×radius
= 2pi×5
= 31.4 cm
Area = pi × r square
= 25 pi
= 78.53cm2
what should be the rate of simpe interest such that the interest is double of the sun at 10 years
Answer:
you never showed the chocies
Step-by-step explanation:
Intelligence quotients (IQs) on the Stanford-Binet intelligence test are normally distributed with a mean of 100 and a standard deviation of 16.
Use the 68-95-99.7
Rule to find the percentage of people with IQs between 84 and 116.
Answer:
Approximately 68% of people have IQs between 84 and 116.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 100, standard deviation of 16.
Percentage of people with IQs between 84 and 116.
84 = 100 - 16
116 = 100 + 16
So within 1 standard deviation of the mean, which, by the Empirical Rule, is approximately 68%.
Matt and his siblings bought their mom her favorite perfume for her birthday. They gave the cashier $80. The cashier gave them back 1 ten-dollar bill, 1 five-dollar bill, 8 dimes, and 1 nickel as change. How much did the perfume cost?
Answer:
$64.15
Step-by-step explanation:
to solve this problem, first we should figure out how much money that the cashier gave them back, and then subtract that from $80 (which was what Matt and his siblings gave the cashier) to find out how much the perfume cost.
it is given that:
they gave the cashier $80.
the cashier gave them back 1 ten-dollar bill ($10), 1 five-dollar bill ($5), 8 dimes ($0.80 or 80 cents) , and 1 nickel ($0.05 or 5 cents)
$10+$5+$0.80+$0.05=$15.85
the total amount of money that the cashier gave them back is $15.85
to find how much the perfume cost:
$80-$15.85=$64.15
so, the perfume cost $64.15
what is the value of sum of 18 and 3 time the difference of 9 and 5 divided by 2 is subtracted from 30 ?
if u give right answer i will mark u as a brainlist
Answer:
12
Step-by-step explanation:
(18+3)=21
(9-5)=4
4x21=84
84/2=42
42-30=12
Answer:
12
Step-by-step explanation:
((18+3)x(9-5))/2-30
=((21)x(4))/2-30
=(84)/2-30
=42-30
=12
If the volume of the expanding cube is increasing at the rate 24 cm3 / min , how fast is its surface area increasing when the surface area is 216 cm2 ?
Answer:
16 cm^2/min
Step-by-step explanation:
dV/dt=24
V=a^3, differentiate with respect to t
dV/dt=3a^2*da/dt, a^2*da/dt=8
S=6a^2, 216=6a^2. a=6. da/dt=(8/36)
dS/dt=12*a*da/dt=12*(8/6)=16 cm^2/min
The increased availability of light materials with high strength has revolutionized the design and manufacture of golf clubs, particularly drivers. One measure of drivers that result in much longer tee shots is known as the coefficient of restitution of the club. An experiment was performed in which 15 drivers produced by a particular club maker were selected at random and their coefficients of restitution measured. It is of interest to determine if there is evidence to support a claim that the mean coefficient of restitution exceeds 0.82. Assume values to be normally distributed. The following observations were obtained for the 15 drivers:
0.8411 0.8191 0.8182 0.8125 0.8750
0.8580 0.8532 0.8483 0.8272 0.7983
0.8042 0.8730 0.8282 0.8359 0.8660
Conduct the test using a significance level of 0.05.
Answer:
WE reject the Null and conclude that the mean coefficient of restitution exceeds 0.82
Step-by-step explanation:
This is a one sample t test :
The hypothesis :
H0 : μ = 0.82
H0 : μ > 0.82
Given the sample data:
0.8411 0.8191 0.8182 0.8125 0.8750
0.8580 0.8532 0.8483 0.8272 0.7983
0.8042 0.8730 0.8282 0.8359 0.8660
Sample size, n = 15
Sample mean = ΣX / n = 0.837
Sample standard deviation, s = 0.0246 (from calculator)
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (0.837 - 0.82) ÷ (0.0246/√(15))
T = 2.676
The critical value at α = 0.05
df = n - 1 ; 15 - 1 = 14
Tcritical(0.05, 14) = 1.761
Reject H0 if Test statistic > Tcritical
Since, 2.676 > 1.761 ; WE reject the Null and conclude that the mean coefficient of restitution exceeds 0.82
please help, will give brainliest!!
Answer:
3
Step-by-step explanation:
[tex] \frac{3x - 3}{x} \div \frac{x - 1}{x} [/tex]
[tex] \frac{3(x - 1)}{x} \times \frac{x}{x - 1} = 3[/tex]
Determine the indicated term in the following arithmetic sequences.
1.) a subscript 5: {2, 5, 8, ...}
2.) a subscript 20: {4, 8, 12, ...}
3.) a subscript 18: {0,20,40,60, ...}
Answer:
[tex]a_5= 14[/tex]
[tex]a_{20}= 80[/tex]
[tex]a_{18}= 340[/tex]
Step-by-step explanation:
Solving (a):
We have:
[tex]a_1=2[/tex] --- first term
[tex]d = 5 -2 = 3[/tex] common difference
The 5h term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_5= 2+ (5 - 1)*3[/tex]
[tex]a_5= 14[/tex]
Solving (b):
We have:
[tex]a_1 = 4[/tex] --- first term
[tex]d = 8 -4 = 4[/tex] common difference
The 20h term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_{20}= 4+ (20 - 1)*4[/tex]
[tex]a_{20}= 80[/tex]
Solving (c):
We have:
[tex]a_1 = 0[/tex] --- first term
[tex]d = 20 -0 = 20[/tex] common difference
The 18th term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_{18}= 0+ (18 - 1)*20[/tex]
[tex]a_{18}= 340[/tex]
Banking fees have received much attention during the recent economic recession as bankslook for ways to recover from the crisis. A sample of 31 customers paid an average fee of $11.53 permonth on their checking accounts. Assume the population standard deviation is $1.50. Calculatethe margin of error for a 90% confidence interval for the mean banking fee.
Answer:
The margin of error for a 90% confidence interval for the mean banking fee is of $0.44.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Sample of 31:
This means that [tex]n = 31[/tex]
Assume the population standard deviation is $1.50.
This means that [tex]\sigma = 1.5[/tex]
Calculate the margin of error for a 90% confidence interval for the mean banking fee.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.645\frac{1.5}{\sqrt{31}}[/tex]
[tex]M = 0.44[/tex]
The margin of error for a 90% confidence interval for the mean banking fee is of $0.44.
Solve for x.
A. 2
B. 5
C. 0
D. 7
Answer:
We know that the angle which lineer and divided by |AB| equal to 130°
Step-by-step explanation:
if 130° look at the 2x+260 we can say that 2x+260=260° so X equal to Zero (0)
Side XY of triangle XYZ is extended to point W, creating a linear pair with ∠WYZ and ∠XYZ.
Triangle X Y Z. Point W extends from side X Y. Angle Z is 36 degrees, angle Y is x degrees, and exterior angle W Y Z is 100 degrees.
What is the value of x?
Answer:
[tex]x= 80^o[/tex]
Step-by-step explanation:
Given
[tex]\angle Z = 36^o[/tex]
[tex]\angle WYZ = 100^o[/tex]
Required
Find x
[tex]\angle WYZ[/tex] and x are on a straight line.
So:
[tex]\angle WYZ + x= 180^o[/tex]
Make x the subject
[tex]x= 180^o -\angle WYZ[/tex]
Substitute known value
[tex]x= 180^o -100^o[/tex]
[tex]x= 80^o[/tex]
Answer:
80 is correct
Step-by-step explanation:
Issac put $5 in a shoe box every day for the months of april, may, and june. He then spent 75% of the money on baseball cards. How much money is left in his shoe box.
please help solve for y!
As both angles are supplementary
[tex]\\ \Large\sf\longmapsto 3x+(2x+3y)=180°[/tex]
[tex]\\ \Large\sf\longmapsto 3x+2x+3y=180[/tex]
[tex]\\ \Large\sf\longmapsto 5x+3y=180[/tex]
[tex]\\ \Large\sf\longmapsto 3y=180-5x[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5x}{3}[/tex]
And
[tex]\\ \Large\sf\longmapsto 3x=90[/tex]
[tex]\\ \Large\sf\longmapsto x=\dfrac{90}{3}[/tex]
[tex]\\ \Large\sf\longmapsto x=30[/tex]
Now
Putting value[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5x}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5(30)}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-150}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{30}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=10[/tex]
Data was collected on reaction time of both hands for an experiment. 14 out of 27 students had a faster reaction time with their right hand than with their left hand. Using this information, we wish to construct a confidence interval for the proportion of all WCU students that have a faster reaction time with their right hand than with their left hand.
Calculate the lower boundary of a 99% confidence interval.
Give your answer as a decimal rounded to 3 places after the decimal.
Answer:
0.3902
Step-by-step explanation:
The question meets the criteria for the calculation of the confidence interval of a one sample proportion ;
Sample size, n = 27
Number of students with faster reaction time = 14
Phat = x / n = 14 / 27 = 0.6296
The confidence interval is calculated thus :
C. I = Phat ± Zcritical * √[p(1 - p)/n]
Zcritical at 99% = 2.576
C. I = 0.6296 ± 2.576 * √[0.6296(0.3704)/27]
C.I = 0.6296 ± 0.2394042
The lower boundary of C.I = 0.6296 - 0.2394042
Lower boundary = 0.3902
I need Help with Functions
Answer:
[tex] g(4) = \frac{5}{11} [/tex]
Step-by-step explanation:
Given:
[tex] g(x) = \frac{x^2 - 6}{3x + 10}
Required:
g(4)
Solution:
Substitute x = 4 into [tex] g(x) = \frac{x^2 - 6}{3x + 10} [/tex]
Thus:
[tex] g(4) = \frac{4^2 - 6}{3(4) + 10} [/tex]
[tex] g(4) = \frac{16 - 6}{12 + 10} [/tex]
[tex] g(4) = \frac{10}{22} [/tex]
[tex] g(4) = \frac{5}{11} [/tex]
A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?
a. 34 feet
b. 46 feet
c. 24 feet
d. 30 feet
Answer: 24 feet
Step-by-step explanation: i just guessed it on pluto and got it right. please leave a like if it worked
The length of another axis for the given ellipse will be around 25.6125 feet so none of the options will be correct.
What is an ellipse?a regular oval form produced when a cone is cut by an oblique plane that does not intersect the base, or when a point moves in a plane so that the sum of its distances from two other points remains constant.
In another word, an ellipse is a curve that becomes by a point moving in such a way that the sum of its distances from two fixed points is a closed planar curve produced.
General equation of an ellipse
(x 2 / a 2 )+ (y2 / b 2 )= 1
Given that
the plot of land is 40 feet across one axis
so 2a = 40 feet
a = 20 feet
The foci are 16 feet from the center so
c = 16
Now we know that
c = √(b² - a²)
c² = b² - a²
16² = b² - 20²
b = 25.6125
So, the length of the minor axis will be around 25.6125 feet.
To learn more about ellipse,
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Can someone help me out plz
Volume = πr²h
Radius = 3yd
Height = 12yd
Take π = 22/7
Volume = 22/7×3×3×12
= 2376/7
= 339.4285714yd³
Rounding off to nearest tenth
= 339.43yd³
Answered by Gauthmath must click thanks and mark brainliest
A line passes through the point (-4, -6) and has a slop of 5. Write an equation for this line.
What does -3/8 > -1 indicate about the positions of -3/8 and -1 on the number line?!
Answer:
-3/8 is located on the right of -1
Step-by-step explanation:
-3/8 is left of -1 because -3/8 is larger than -1.
s A lottery offers one 800 prize, one 700 Prize, two 800 prizes, and four prizes. One thousand tickets are sold at each. Find the expectation if a person buys two tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.
The question is incomplete. The complete question is :
A lottery offers one $800 prize, one $700 Prize, two $800 prizes, and four $100 prizes. One thousand tickets are sold at $5 each. Find the expectation if a person buys two tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.
The expected if a person buys two tickets is $__
Answer:
$ -1.52
Step-by-step explanation:
Given :
A lottery offers --
One $800 prize
One $700 prize
Two $800 prize
Four $100 prizes
Let X = net win
X P(X)
795 1/1000
695 1/1000
795 2/1000
95 4/1000
-5 996/1000
[tex]$E(X) = \sum X \ p(X)$[/tex]
[tex]$=795 \times \frac{1}{1000} + 695 \times \frac{1}{1000} + 795 \times \frac{2}{1000} + 95 \times \frac{4}{1000} + (-5) \times \frac{996}{1000}$[/tex]
= 0.795 + 0.695 + 1.59 + 0.38 - 4.98
= $ -1.52
Consider the expressions 7y + 5 − 3 and 7y + 2. Which statement is true?
Answer:
A.
Step-by-step explanation:
Start with
7y + 5 - 3
Combine like terms:
7y + 2
By combining like terms in 7y + 5 - 3, we end up with 7y + 2 which is the second expression.
Therefore, the expressions are equivalent because they evaluate to equal values for every value of y.
Answer: A.
share the following total in its given ratio. $18 at ratio 1.2
Find the area enclosed in the graph of
x² + y² 16x + 32y.
Answer:
3
256
sq.units
Step-by-step explanation:
Both parabolas cut each other at (0,0) and (16,16)
Area enclosed by these parabolas
=∫
0
16
4
x
dx−∫
0
16
16
x
2
dx
=[
3
2×4×x
3/2
]
0
16
−[
16×3
x
3
]
0
16
=
3
2×4
4
−
3
4
4
=
3
256
sq. units
