Answer:
The function is exponential.
The function increases by a factor of 2.5 for each unit increase in x.
The domain of the function is all real numbers
The true statements are:
[tex]\mathbf{y = 3(2.5)^x}[/tex] is an exponential functionThe function represents an exponential growthThe domain of the function is the set of all real numbersThe function is given as:
[tex]\mathbf{y = 3(2.5)^x}[/tex]
An exponential function is represented as:
[tex]\mathbf{y = ab^x}[/tex]
Where: a represents the initial value, and b represents the rate
This means that:
[tex]\mathbf{y = 3(2.5)^x}[/tex] is an exponential function
By comparison:
[tex]\mathbf{b = 2.5}[/tex]
When b > 0, then the function represents an exponential growth
2.5 is greater than 0.
So, the function represents an exponential growth
Lastly, there is no restriction to the values of x.
So, the domain of the function is the set of all real numbers
Read more about exponential functions at:
https://brainly.com/question/11487261
A courier service claims that 5% of all of its deliveries arrive late. Assuming the claim is true and deliveries are independent, a sample of 10 deliveries is randomly selected. What is the probability that more than 2 of the sample deliveries arrive late
Answer:
The probability that more than 2 of the sample deliveries arrive late = 0.0115
Step-by-step explanation:
This is a binomial distribution problem
A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.
It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure. The outcome of each trial/run of a binomial experiment is independent of one another.
The probability of each delivery arriving late = 5% = 0.05
- Each delivery is independent from the other.
- There is a fixed number of deliveries to investigate.
- Each delivery has only two possible outcomes, a success or a failure of arriving late.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of deliveries we're considering = 10
x = Number of successes required = number of deliveries that we expect to arrive late = more than 2 = > 2
p = probability of success = probability of a delivery arriving late = 0.05
q = probability of failure = probability of a delivery NOT arriving late = 0.95
P(X > 2) = 1 - P(X ≤ 2)
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 0.59873693924 + 0.31512470486 + 0.07463479852
= 0.98849644262
P(X > 2) = 1 - P(X ≤ 2)
= 1 - 0.98849644262
= 0.01150355738
= 0.0115
Hope this Helps!!!
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
81.64
Step-by-step explanation:
To find the circumference of this circle we take pi or 3.14 and multiply it by 2
3.14 * 2 = 6.28
Then we multiply 6.28 by 13
6.28 * 13 = 81.64
Which is the graph |3x-6|=21
Answer:
it should look like this
Diana works in a building that is 130 feet tall. She is outside, looking up at the building at an angle of 37° from her feet to the top of the building. If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? Round the answer to the nearest tenth of a foot.
Answer:
Let x be her initial distance from the building, then tan 37 = 130/x
x = 130/tan 37 = 130/0.7536 = 172.5 feet
Let y be her distance from the building after moving forward, then
tan 40 = 130/y
y = 130/tan 40 = 130/0.8391 = 154.9
After moving forward, she is 172.5 - 154.9 = 17.6 ft closer.
Answer: B. 17.6 ft.
Step-by-step explanation: I just did it on the edge 2023 assignment. Check attached image.
In the multiplication sentence below, which numbers are the factors? Check
all that apply.
10 x 8 = 80
A. 80
B. 8.
I C. 10
Answer:
10 and 8
Step-by-step explanation:
10 and 8 are the factors in this equation because factors are the numbers that are mutiplied together to get the product (The answer to a mutiplication problem) Therefore the factors in this equation are 10 and 8 because those are the numbers that are mutiplied together to get the product.
angle ∠DAC= angle ∠BAD. What is the length of BD? Round to one decimal place.
Answer: 3.9
Step-by-step explanation: Khan Academy
The length of BD if The angle ∠ DAC is equal to the angle ∠ BAD is 3.92.
What is the triangle?Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.
Given:
The angle ∠ DAC = angle ∠ BAD
As we can see that the triangle BAD and triangle DAC are similar By SAS similarity,
AC / AB = CD / BD (By the proportional theorem of similarity)
5.6 / 5.1 = 4.3 / BD
1.09 = 4.3 / BD
BD = 4.3 / 1.09
BD = 3.92
Thus, the length of BD is 3.92.
To know more about Triangles:
https://brainly.com/question/16886469
#SPJ2
Joe wants to saw a wooden plank into 3/4 -meter pieces. The length of the wooden plank is 15/4meters. How many 3/4 -meter pieces can Joe saw from the wooden plank?
Answer:
3 wooden plank he can saw
Answer:
he can saw 3 wooden planks
Step-by-step explanation:
Find two consecutive even integers whose sum is -50. Which of the following equations could be used to solve the problem? A) 2 x + 2 = -50 B) 2 x = -50 C) 2 x + 1 = -50 D) x^2 + 1= -50
Answer:
[tex]2x+2=-50[/tex]
Step-by-step explanation:
[tex]x+2=y\\x+y=-50\\x+x+2=-50\\2x+2=-50[/tex]
The equation that can be used to find out [tex]x[/tex] and [tex]y[/tex] is [tex]2x+2=-50[/tex]
Answer:
[tex]\mathrm{A}[/tex]
Step-by-step explanation:
Two consecutive even integers.
The first integer is even and can be as [tex]x[/tex]
The second integer is also even and can be as [tex]x+2[/tex]
Their sum is [tex]-50[/tex]
[tex]x+x+2=-50[/tex]
[tex]2x+2=-50[/tex]
QHome Spring 2020
Major arc JL measures 300
Which describes triangle JLM?
300
right
obtuse
K
M.
scalene
O equilateral
Answer:
(D)Equilateral Triangle
Step-by-step explanation:
Given a circle centre M; and
The measure of major arc JL = 300 degrees
The triangle formed by radii ML and MJ and chord JL is Triangle JLM.
Since ML=MJ (radii of a circle), the base angles are equal.
Therefore:
[tex]\angle MLJ= \angle MJL\\\angle LMJ =60^\circ\\$Therefore:\\\angle LMJ+2\angle MLJ=180^\circ\\60^\circ+2\angle MLJ=180^\circ\\2\angle MLJ=180^\circ-60^\circ\\2\angle MLJ=120^\circ\\\angle MLJ=60^\circ[/tex]
We can see that all the angles of triangle JLM are 60 degrees, therefore Triangle JLM is an Equilateral Triangle.
A zorb is a large inflated ball within a ball. The formula for the radius r of a sphere with surface area A is given by requalsStartRoot StartFraction Upper A Over 4 pi EndFraction EndRoot . Calculate the radius of a zorb whose outside surface area is
Answer:
radius r of the zorb is ≅ 1.40 m
Step-by-step explanation:
GIven that;
the radius r of a sphere with surface area A is given by;
[tex]r = \sqrt{\dfrac {A}{4 \pi }}[/tex] which is read as : (r equals StartRoot StartFraction Upper A Over 4 pi EndFraction EndRoot .)
We are to calculate the radius of a zorb whose outside surface area is 24.63 sq ( the missing part of the question)
Given that the outside surface area is : 24.63 sq
Let replace the value of the outside surface area which 24.63 sq for A in the equation given from above.
SO: A = 24.63 sq
[tex]r = \sqrt{\dfrac {A}{4 \pi }}[/tex]
[tex]r = \sqrt{\dfrac {24.63}{4 \pi }}[/tex]
[tex]r = \sqrt{1.9599}[/tex]
r = 1.399
radius r of the zorb is ≅ 1.40 m
Expand 2x(5x-2)
Help please ?
Answer: 10x^2 - 4x
Step-by-step explanation:
To expand, you are not simplifying, so multiplying out is the answer here. To do this, use the distributive property. The distributive property in this case means that if you are multiplying one number by a whole expression inside parenthesis, multiply the one number by each term in the expression:
2x(5x - 2)
= 2x(5x) + 2x(-2)
= 10x^2 - 4x
The product of the expression is equivalent to -
10x² - 4x.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as follows -
2x(5x - 2)
The given expression is -
2x(5x - 2)
10x² - 4x
Therefore, the product of the expression is equivalent to -
10x² - 4x.
To solve more questions on expression evaluation, visit the link below -
brainly.com/question/1041084
#SPJ5
Nicola runs a small pottery cafe. Customers choose from a range of ceramics which they paint and personalise.
Nicola wants to make as much profit as possible on the sale of ceramic plates. She pays £1.28 for each plate. What is the most profit Nicola can make on one plate.
Answer:
Bb
Step-by-step explanation:
The mean amount of time it takes a kidney stone to pass is 13 days and the standard deviation is 5 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.
Answer:
X ~ Norm ( 13 , 25 )
P ( X > 17 ) = 0.2119
16.37 days
Step-by-step explanation:
Solution:-
- We are given a distribution for the amount of time for a kidney stone to pass.
- The distribution is parameterize by the mean time taken ( u ) and the standard deviation ( s ) as follows:
u = 13 days
s = 5 days
- Here, we will define a random variable X: The time taken by a kidney stone to pass to be normally distributed with parameters ( u ) and ( s ). We express the distribution in the notation form as follows:
X ~ Norm ( u , s^2 )
X ~ Norm ( 13 , 25 )
- We are to determine that a randomly selected individual takes more than 17 days for the stone to pass through.
- We will first standardize the limiting value for the required probability by computing the Z-score as follows:
[tex]Z-score = \frac{X - u}{s} \\\\Z-score = \frac{17 - 13}{5} \\\\Z-score = 0.8[/tex]
- We will use the standard normal table to determine the probability of kidney stone passing in less than 17 days ( Z = 0.8 ); hence, we have:
P ( X < 17 ) = P ( Z < 0.8 )
P ( X < 17 ) = 0.7881
- To compute the probability of an individual taking more than 17 days would be " total probability - P ( X < 17 ) as follows" . Where the total probability of any distribution is always equal to 1.
P ( X > 17 ) = 1 - P ( X < 17 )
P ( X > 17 ) = 1 - 0.7781
P ( X > 17 ) = 0.2119
- Nest we are to determine the amount of days it would take for an individual to lie in the upper quarter of the spectrum. We can interpret this by looking at the limiting value corresponding to the P ( X > x ) = 0.25.
- The upper quartile of any distribution amounts to probabilities: " > x = 0.25 " or " < x = 0.75 ".
- We will use the standard normal table for ( Z-score ) and look-up the Z-score value corresponding to P ( Z < a ) = 0.75 as follows:
P ( Z < a ) = 0.75
a = 0.674
- Now we will use the standardizing formula used in previous part and compute the value of "x" associated with the limiting Z-score value:
[tex]Z-score = \frac{x-u}{s} = 0.674\\\\x = 0.674*s + u\\\\x = 0.674*5 + 13\\\\x = 16.37[/tex]
Answer: It would should take more than 16.37 days for an individual if he is to lie in the upper quartile of the defined distribution.
Solve the equation and express each solution in a+bi form x^4-7x^2-8=0
Answer:
x = ±2√2, ±i
Step-by-step explanation:
Step 1: Factor
(x² - 8)(x² + 1)
Step 2: Find roots
x² - 8 = 0
x² = 8
x = ±2√2
x² + 1 = 0
x² = -1
x = ±i
Answer:
The answer is B
Step-by-step explanation:
Antipsychotic drugs are widely prescribed for conditions such as schizophrenia and bipolar disease. An article reported on body composition and metabolic changes for individuals who had taken various antipsychotic drugs for short periods of time. (a) The sample of 41 individuals who had taken aripiprazole had a mean change in total cholesterol (mg/dL) of 3.55, and the estimated standard error sD n was 3.478. Calculate a confidence interval with confidence level approximately 95% for the true average increase in total cholesterol under these circumstances. (Round your answers to two decimal places.)
Answer:
95% for the true average increase in total cholesterol under these circumstances
(-2.306 , 9.406)
Step-by-step explanation:
Step(i):-
Given sample size 'n' =41
Mean of the sample(x⁻) = 3.55
The estimated standard error
[tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]
Given estimated standard error ( S.E) = 3.478
Level of significance ∝=0.05
Step(ii):-
95% for the true average increase in total cholesterol under these circumstances
[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]
Degrees of freedom
ν= n-1 = 41-1 =40
t₀.₀₅ = 1.6839
95% for the true average increase in total cholesterol under these circumstances
[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]
( 3.55 - 1.6839 ×3.478 ,3.55 + 1.6839 ×3.478 )
(3.55 - 5.856 , 3.55 + 5.856)
(-2.306 , 9.406)
Conclusion:-
95% for the true average increase in total cholesterol under these circumstances
(-2.306 , 9.406)
Please answer this correctly
Pleassseee hhheeelllppp
Answer/Step-by-step explanation:
When solving problems like this, remember the following:
1. + × + = +
2. + × - = -
3. - × + = -
4. - × - = +
Let's solve:
a. (-4) + (+10) + (+4) + (-2)
Open the bracket
- 4 + 10 + 4 - 2
= - 4 - 2 + 10 + 4
= - 6 + 14 = 8
b. (+5) + (-8) + (+3) + (-7)
= + 5 - 8 + 3 - 7
= 5 + 3 - 8 - 7
= 8 - 15
= - 7
c. (-19) + (+14) + (+21) + (-23)
= - 19 + 14 + 21 - 23
= - 19 - 23 + 14 + 21
= - 42 + 35
= - 7
d. (+5) - (-10) - (+4)
= + 5 + 10 - 4
= 15 - 4 = 11
e. (-3) - (-3) - (-3)
= - 3 + 3 + 3
= - 3 + 9
= 6
f. (+26) - (-32) - (+15) - (-8)
= 26 + 32 - 15 + 8
= 26 + 32 + 8 - 15
= 66 - 15
= 51
A jar of marbles contains the following: two purple marbles, four white marbles, three blue marbles, and two green marbles. What is the probability of selecting a white marble from a jar of marbles?
Answer:
4/11
Step-by-step explanation:
Total number of marbles = 2(purple) + 4(white) + 3(blue) + 2(green)
= 11
Number of white marbles = 4
Probability of selecting a white marble =
number of white marbles/total number of marbles in the jar
= 4/11
The probability of selecting a white marble from a jar of marbles is 4/11.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Purple Marbles = 2
White Marbles = 4
Blue Marbles = 3
Green Marbles = 2
Total marbles= 2+ 4+ 3+ 2= 11
So, the probability of selecting a white marble from a jar of marbles
= 4/11
Hence, the probability is 4/11.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ2
Find one positive angle and one negative angle that is coterminal with the given angle of 300 degrees
Step-by-step explanation:
positive angle =300+180=480.
negative angle = 300 -180=120
someone help please with this question
Step-by-step explanation:
1. 180 - (36 +36)= 108
2. angle ABC = 108 angle DBC = 108-72=36
3. angle DCB=angle DBC. This is because the base angles are equal
4 therefore triangle BDC is isoscles
Answer:
Because ΔABD is isosceles, ∠ABD ≅ ∠ADB = 72° because of Base Angles Theorem which states that the base angles of an isosceles triangle are congruent. Then, ∠BDC = 180° - ∠ADB = 108° because they are supplementary angles. Because ΔABC is isosceles, ∠BAC ≅ ∠BCA = 36° because of Base Angles Theorem, which means ∠CBD = 180° - 108° - 36° = 36° because of the sum of angles in a triangle. Therefore, ΔBCD is isosceles because of the Converse of Base Angles Theorem.
Luke and skylar work at furniture store. Luke is paid $180 per week plus 5% of his total sales in dollars ,x,which can be represented by g(x)=180+0.05x. Skylar is paid $104 per week plus 7% of her total sales in dollars which can be represented by f(x)=104+0.07x. Determine the value of x in dollars that will make their weekly pay the same
Answer:
The total sales in dollars to make their pay equal is: $ 3800
Step-by-step explanation:
Since we need to find the number of sales that make both function equal in value, we equal both expressions, and solve for 'x":
[tex]180+0.05 \,x=104+0.07 \,x\\180-104=0.07\,x-0.05\,x\\76=0.02x\\x=\frac{76}{0.02} \\x=3800[/tex]
HELP ASAP GIVING BRANLIST!!
Answer:
Question 1: 3 - 5 hours.
Question 2: 0 - 1 hour
Step-by-step explanation:
Question 1: As you can see in the diagram, the guy is moving really slowly and is almost stuck, therefore, it is 3 - 5 hours.
Question 2: In hours 0 - 1, you can see that the graph is the closest to vertical as it gets.
A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The 95% confidence interval for the average hourly wage (in $) of all information system managers is
Answer:
The 95% confidence interval for the average hourly wage of all information system managers is (39.14,42.36)
Step-by-step explanation:
In order to calculate the 95% confidence interval for the average hourly wage we would have to calculate first the margin of error as follows:
ME=t0.05/2,n-1s/√n
for n=75, t0.025,74=1.993
Therefore, ME=1.993*7/√75
ME=1.61
Therefore, the 95% confidence interval for the average hourly income of all syatem manager would be as follows:
(X-ME,X+ME)=(40.75-1.61,40.75+1.61)
=(39.14,42.36)
3z/10 - 4 = -6
someone help?
Answer:
[tex]z=-\frac{20}{3}[/tex]
Step-by-step explanation:
[tex]\frac{3z}{10}-4=-6\\\\\frac{3z}{10}-4+4=-6+4\\\\\frac{3z}{10}=-2\\\\\frac{10\cdot \:3z}{10}=10\left(-2\right)\\\\3z=-20\\\\\frac{3z}{3}=\frac{-20}{3}\\\\z=-\frac{20}{3}[/tex]
Best Regards!
The average height of students at UH from an SRS of 12 students gave a standard deviation of 2.5 feet. Construct a 95% confidence interval for the standard deviation of the height of students at UH. Assume normality for the data.a. (1.271, 6.245)b. (0.771, 10.245)c. (1.771, 4.245)d. (7.771, 9.245)e. (4.771, 10.245)f. None of the above
Answer:
c. [1.771;4.245] feet
Step-by-step explanation:
Hello!
The variable of interest is
X: height of a student at UH
X~N(μ;σ²)
You have to estimate the population standard deviation using a 95% confidence interval.
The statistic to use for the interval is a student Chi-Square with n-1 degrees of freedom. First you have to calculate the CI for the population variance:
[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]
[tex]X^2_{n-1;1-\alpha /2}= X^2_{11;0.975}= 21.920[/tex]
[tex]X^2_{n-1;\alpha /2}= X^2_{11;0.025}= 3.816[/tex]
n=12
S= 2.5
[tex][\frac{11*6.25}{21.920} ;\frac{11*6.25}{3.816}} ][/tex]
[3.136; 18.016] feet²
Then you calculate the square root of both limits to get the CI for the population standard deviation:
[√3.136; √18.016]
[1.771;4.245] feet
I hope this helps!
HELP ASAP!!!The first picture is what each variables equal too
Answer:
Just replace the variables with the number
d5
c4 (uh oh)
a2
b-3
f-7
d-c = 5 - 4 = 1
1/3 - 4(ab+f)
2 x -3 = -6
-6 + -7 = -13
-13 x 4 = -52
1/3 - -52 = 1/3 + 52 =
52 1/3
Hope this helps
Step-by-step explanation:
You buy 144 inches of ribbon at 15 cents per yard and 3 1/2 pounds of tomatoes at 48 cents per pound. What is your change from a $20 bill? (SHOW YOUR WORK).
Answer:
$17.72 left
Step-by-step explanation:
144 inches = 4 yards
4(0.15) + 3.5(0.48) = 0.6 + 1.68 = $2.28 SPENT
20 - 2.28 = $17.72 left in change
A grocery store manager notices that this month her store sold a total of 597 gallons of ice cream, which represents a decrease of 15% from last month. On the other hand, her store sold 617 pounds of broccoli this month, which represents an increase of 21% from last month. How much ice cream and broccoli did the store sell last month? Round your answers to the nearest integer.
Answer:
(a)The total sales of ice-cream last month is 702 gallons.
(b)The total sales of broccoli last month is 510 pounds.
Step-by-step explanation:
Part A
Total Sales of gallons of ice cream this month = 597
Since it represents a decrease of 15% of last month's sales
Let the total sales of ice-cream last month =x
Then:
(100-15)% of x =597
85% of x=597
0.85x=597
x=597/0.85
x=702 (to the nearest integer)
The total sales of ice-cream last month is 702 gallons.
Part B
Total Sales of broccoli this month = 617 pounds
Since it represents an increase of 21% of last month's sales
Let the total sales of ice-cream last month =y
Then:
(100+21)% of y =617
121% of y=617
1.21y=617
y=617/1.21
y=510 (to the nearest integer)
The total sales of broccoli last month is 510 pounds.
The scores on the Wechsler Adult Intelligence Scale are approximately Normal with \muμ = 100 and \sigmaσ = 15. If you scored 130, your score would be higher than approximately what percent of adults?
Answer:
Your score would be higher than 97.72% of adults, that is, higher than approximately 98% of adults.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 100, \sigma = 15[/tex]
If you scored 130, your score would be higher than approximately what percent of adults?
To find the proportion of scores that are lower than, we find the pvalue of Z when X = 130. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{130 - 100}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
0.9772*100 = 97.72%.
Your score would be higher than 97.72% of adults, that is, higher than approximately 98% of adults.
the answer is 15 hours what is the question
Answer:
how many hours do you spend on your laptop
Answer:
the question is 17 hours - 2 hours