The provided arithmetic sequence adds up to 60.
What is an arithmetic sequence?The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the sequence. The nth term of an arithmetic sequence is given by. aₙ = a + (n – 1)d
Given an arithmetic sequence 12, 14,16,18
The general formula for the Sum of arithmetic sequence:
Sn = n/2 [2a+(n−1)d]
where: n = the number of terms to be added.
a = the first term in the sequence.
d = the constant value between terms.
In our case,
a = 12
n = 4
and d = 14 - 12 = 2
thus
Sum = 4/2(2*12 + (4- 1 )2)
Sum = 2( 24 + 6)
Sum = 60
therefore, the Sum of the given Arithmetic sequence is 60.
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Find x.... Figure is not drawn to scale.
Answer:
33.
Step-by-step explanation:
I assume that the 2 triangles are similar.
x/77 = 24/56
56x = 77*24
x = (77*24(/56
x = 33.
Simon score 4x10^2 points in a game. Joe scored 2x10^3 points in the same game. whose score is higher? how much higher?
Answer:
Joe scored higher by 1600
Step-by-step explanation:
Given
[tex]Simon = 4 * 10^2[/tex]
[tex]Joe = 2 * 10^3[/tex]
Solving (a): Which is higher?
First, we need to convert both numbers to whole numbers
[tex]Simon = 4 * 100[/tex]
[tex]Simon = 400[/tex]
[tex]Joe = 2 * 10^3[/tex]
[tex]Joe = 2 * 1000[/tex]
[tex]Joe = 2000[/tex]
2000 is greater than 400;
Hence, Joe score higher
Solving (b): By how much?
We simply calculate the difference
[tex]Difference = Joe - Simon[/tex]
[tex]Difference = 2000 - 400[/tex]
[tex]Difference = 1600[/tex]
Which equation expresses d in terms of t and a?
Answer:
Option D
Step-by-step explanation:
I got it right
Question 2 (10 points) (02.05 MC) Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P′Q′R′ has vertices P′(4, 0), Q′(3, 1), and R′(−1, −2). Plot triangles PQR and P′Q′R′ on your own coordinate grid. Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points) Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points) Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)
Answer: From R:(c, d), draw line segment RA perpendicular to the x-axis. Let O denote the origin (0,0).
area ΔPQR = area trapezoid OPRA- area ΔQAR - area ΔOPQ
=
2
1
c(a+d) -
2
1
d(c−b)-
2
1
ab=
2
1
(ac+bd−ab).
If c area ΔPQR = area trapezoid OPRA + area Δ QAR - areaΔOPQ=
2
1
c(a+d)
2
1
d(b−c)−
2
1
ab=
2
1
(ac+bd−ab).
Step-by-step explanation: done
A pumpkin grows with a constant of proportionally of 4 cm in diameter per week. If Susan begins growing her pumpkin 10 weeks before Halloween will her pumpkin be larger that 50 cm in diameter?
2. Arsenic is a compound that occurs naturally in very low concentrations. Arsenic blood concentrations in healthy individuals are Normally distributed, with a mean of 3.2 mg/dl and a standard deviation of 1.5 mg/dl. A researcher believes that one area of the United States has naturally elevated arsenic levels in the ground and water supplies. An SRS of 25 individuals in this area found a sample mean arsenic level of 3.75 mg/dl. What are the null and alternative hypotheses for this study?
Answer:
The null hypothesis [tex]H_o : \mu = 3.2 \ mg/dl[/tex]
The alternative hypothesis [tex]H_a : \mu > 3.2 \ mg/dl[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 3.2 \ mg/dl[/tex]
The standard deviation is [tex]\sigma = 1.5 mg/dl[/tex]
The sample size is n = 25
The sample mean is [tex]\= x = 3.75 \ mg /dl[/tex]
Generally
The null hypothesis is : That the mean of the Arsenic blood concentrations in healthy individuals is [tex]\mu = 3.2 \ mg/dl[/tex]
i.e
The null hypothesis [tex]H_o : \mu = 3.2 \ mg/dl[/tex]
The alternative hypothesis is : That the mean of the Arsenic blood concentrations in healthy individuals is greater than [tex]\mu = 3.2 \ mg/dl[/tex]
The alternative hypothesis [tex]H_a : \mu > 3.2 \ mg/dl[/tex]
ANSWER PLEASE NEED HELP ASAP
Answer: 43 should be divided into 0.37 to find “x”.
Step-by-step explanation:
4(3x + 1)
What is the answer to 4(3x + 1)
Answer:
Answer is 12x+4. Hope that helped.
Round 24,837,618 to the ten thousands place. I’m on math college so I need help on this problem!
Answer:
24,840,000
Step-by-step explanation:
Round up of numbers includes rounding them up to a given place value.
We are asked to round 24,837,618 to the ten thousands place.
The ten thousands place is the place where the number 3 in the number is located.
The number after 3 = 7 is a number above 5. Hence, we add 1 to 3, making it 4
Therefore, 24,837,618 to the ten thousands place is 24,840,000
Maria found the least common multiple of 6 and 15. Her work is shown below.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,...
Multiples of 15:15, 30, 45, 60, ...
The least common multiple is 60.
What is Maria's error?
Answer:
answer B
Step-by-step explanation:
just got it right on the test.
Answer:
the answer is B, Maria listed factors of each number instead of multiples.
Step-by-step explanation:
Consider a conical tank, where the height of the tank is 12 meters, and and the diameter of the tank at the top is 8 meters. Water is leaking out of the bottom of a conical tank at an constant rate of 20,000 LaTeX: \text{cm}^3 / \text{min}cm 3 / min. Water is also being pumped in to the tank at a constant unknown rate (call it LaTeX: kk). The water level is currently 8 meters high, and the water level is rising at a rate of 2 LaTeX: \text{cm} / \text{min}cm / min. Find the rate LaTeX: kk at which water is being pumped in to the tank.
Answer:
The answer is below
Step-by-step explanation:
The height of tank = 12 m = 1200 cm, the diameter of the tank = 8 meters, hence the radius of the tank = 8/2 = 4 m = 400 cm
Let h represent the water level = 8 m = 800 cm. The radius (r) of the water level at a height of 8 m is:
r/h = radius of tank/ height of tank
r/h = 400/1200
r = h/3
[tex]\frac{change\ in\ volume}{change\ in \ time}=water\ in-water\ out\\ \\\frac{dV}{dt=} water\ in-water\ out\\\\V=\frac{1}{3}\pi r^2h\\ \\r=\frac{1}{3}h \\\\V=\frac{1}{3}\pi (\frac{1}{3}h )^2h\\\\V=\frac{1}{9} \pi h^3\\\\\frac{dV}{dt} =\frac{1}{3} \pi h^2\frac{dh}{dt}\\\\\frac{dh}{dt}=2\ cm/min,h=8\ m=800\ cm\\\\[/tex]
[tex]\frac{dV}{dt} =\frac{1}{3} \pi (800)^2(2)=426666.7\ cm^3/min\\\\\frac{dV}{dt=} water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-20000\ cm/min\\ \\water\ in=426666.7\ cm^3/min+20000\ cm/min\\\\water\ in=446666.7 \ cm^3/min[/tex]
1. The perimeter of a rectangular field is 180 feet. Let x be the length of the field (in feet) and let y be the width (in feet). Write an equation to model the perimeter of the rectangular field.
Also this question so there's 2 questions
2. Tyrone is designing a rectangular sandbox. He wants the sandbox to be 15 feet long and have a perimeter of 46 feet. How wide does Tyrone’s sandbox need to be?
Answer:
1. 2(x + y) = 180
2. His sandbox needs to be 8 ft wide.
Researchers tracked 2668 people from early childhood through adulthood and found that 13-year-olds who are frequent
targets of bullies were three times more likely than their non-victimized peers to be depressed later as adults.
Identify the population, sample, and variables for the study.
Answer:
Step-by-step explanation:
(A) The population is the 2,668 people who were tracked from early childhood to adulthood.
(B) The sample comprised all 13-year olds within the population. Since the members of the population started out as kids (and later became adults), the sample was inclusive of all 2,668 individuals but only at the age of 13. That is where the focus was; at the age of 13.
The study then proceeded to divide them into two groups - the experimental group (13 year olds who were frequent targets of bullies) and the non-experimental group (13 year olds who were not frequent targets of bullies).
(C) The variables in this study are:
- 13 year olds who were frequent targets of bullies
- 13 year olds who were not frequent targets of bullies
- Adults (from the same population who were once 13 year olds) with depression
- Adults (from the same population who were once 13 year olds) without depression.
NOTE HOWEVER that the degree of bullying each teenager faced and the magnitude of depression each adult faced, can be gotten from the above variables; when they assume a figure or number which can be high, low or medium.
Rewrite the equation in standard form.
y=2x-10
Answer:
The equation in standard form:
2x-y-10=0
(I’m sorry for the horrible quality but please help ASAP) which proportion can be used to show that the slope of PR Is equal to the slope of rt?
Answer:
Correct option: F.
Step-by-step explanation:
The slope of a line
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
To show the slope of PR is equal to the slope of RT, we'll use the extreme points of each segment.
For PR, use P=(-7,7) R=(-4,3). Now calculate the slope
[tex]\displaystyle m=\frac{3-7}{-4-(-7)}[/tex]
For RT, use R=(-4,3) (2,-5). Calculate the second slope:
[tex]\displaystyle m=\frac{-5-3}{2-(-4)}[/tex]
If both slopes are equal, then:
[tex]\displaystyle m=\frac{3-7}{-4-(-7)}=\frac{-5-3}{2-(-4)}[/tex]
Correct option: F.
Mandy, Carly, and Armond collect sports jerseys. Carly has 5 more jerseys than Mandy, and
Armond has three times as any jerseys as Carly. Altogether, they have 80 jerseys. Find the
number of jerseys each person has.
(1 Point)
Enter your answer using c for Carly, m for Mandy and a for Armond.
Enter your math answer
Armando and Mikayla have a new grandson. How much money should they invest now so that he
will have $80,000 for his college education in 18 years? The money is invested at 8% compounded
annually
9514 1404 393
Answer:
$20,020
Step-by-step explanation:
The future value formula is helpful.
FV = P(1 +r)^t
$80,000 = P(1.08^18) = 3.9960195P
P = $80,000/3.9960195 = $20,019.92
They should invest about $20,020 now.
question 11 I mark as brainliest
Answer:
32
Step-by-step explanation:
A train travelled a distance of 1350 kilometers in 15 hours find it,s average speed answer pleaseeeeeeeee fast ,thanks
Answer:
90
Step-by-step explanation:
1350 divided by 15
In the past, patrons at a cinema spent an average of $ 2.50 for popcorn with standard deviation of $ 0.90. The amount of these expenditures is normally distributed . Following an intensive public campaign about the negative health effects of eating popcorn by a local medical school, the mean expenditures for a sample of 18 patrons is found to be $ 2.10. At 0.01 level of significance, does this recent experience suggest decline in spending
Answer:
There's no evidence to show that the recent experience suggests a decline in spending.
Step-by-step explanation:
We are given;
Population mean; μ = $2.5
Population Standard deviation; σ = $0.9
Sample mean; x¯ = $2.1
Sample size; n = 18
Significance level; α = 0.01
Let's define the hypothesis;
Null hypothesis; H0: μ ≥ $2.5
Alternative hypothesis; Ha: μ < $2.5
z-score formula is;
z = (x¯ - μ)/(σ/√n)
z = (2.1 - 2.5)/(0.9/√18)
z = -0.4/0.2121
z = -1.886
Using the p-value from z-score calculator attached and using z = -1.886; α = 0.01; one tail; we have;
P-value = 0.2965
This is more than the significance level. Thus, we will fail to reject the null hypothesis and conclude that there is no evidence to show that the recent experience suggests a decline in spending.
whats the answer of 3/4 + 1/4 =
Answer:
1
Step-by-step explanation:
3/4 + 1/4 since they both have a 4 as the denominator you only have to add the top since they made it easy. and since that would be 4/4 your answer would be 1 whole.
Being tested hurry pls.
All of the following statements about the Jumanos are true except: a. They hunted buffalo. b. They were avid traders. c. They lived along the Rio Grande. d. They still live near El Paso today.
Answer:
b
Step-by-step explanation:
The graph below shows a transformation of y
- 2x
Write the equation for the graph in the comment
Answer:
[tex]y=-2^{(x+2)}+1[/tex]
Step-by-step explanation:
Equation of the parent function of the graph attached is,
y = [tex]2^{x}[/tex]
Let the equation of the transformed function function shown in the graph be,
y = a(2ˣ) + b
Now we will find the values of a and b by substituting the points lying on the curve.
For (-2, 0),
0 = a(2⁻²) + b
[tex]\frac{a}{4}+b=0[/tex] ------(1)
For (0, -3),
-3 = a(2⁰) + b
a + b = -3 --------(2)
Subtract equation (1) from equation (2),
(a + b) - ([tex]\frac{a}{4}+b[/tex]) = 0 + 3
[tex]\frac{3a}{4}=3[/tex]
a = -4
From equation (2),
-4 + b = -3
b = 1
Therefore, equation of the transformed function will be,
[tex]y=-4(2^x)+1[/tex]
[tex]y=-2^{2}(2^x)+1[/tex]
[tex]y=-2^{(x+2)}+1[/tex]
Graph transformation is the process by which an existing graph is modified to produce a variation of the proceeding graph.
Equation of transformed graph is, [tex]y=-2^{x+2}+1[/tex]
Here, equation of original graph is given, [tex]y=2^{x}[/tex]
Let us consider, equation of transformed graph is, [tex]y=m(2^{x} )+n[/tex]
Since, given graph passing through points (-2,0) and (0,-3)
Substituting above points into equation.
We get two equation,
m +4n = 0
m + n = -3
After solving, we get m= -4 and n = 1
So, equation becomes [tex]y=-2^{x+2}+1[/tex]
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HELP PLEASEEEE! suppose the average wait time for a sandwich at a local deli is 5 min with a standard deviation of 3 min. Is it unusual to get a sandwich in only 12 minutes?
A. Yes because 12 min is more than two standard deviations below the mean.
B. No, because 12 min is less than two standard deviations above the mean.
C. No, because 12 min is more then two standard deviations above the mean.
D. Yes because 12 min is more than two standard deviations above the mean.
Answer:
D
Step-by-step explanation:
Here, we want to state if it is unusual or not get a sandwich in 12 minutes given the mean time and the standard deviation.
The answer here is that it is unusual.
The reason why it is unusual is because, two standard deviations above the mean in this case will be 5 + 3 + 3 = 11
Looking at the value given which is 12, we can see that this value is actually greater than the value which is 2 standard deviations above the mean.
What we are saying here is that 12 is greater than two standard deviation above the mean which is valued at 11
24 + 28 as a product of two factors using the GCF and distributive property
Answer:
52
Step-by-step explanation:
Using GCF:
The factors of 24 are; 1, 2, 3, 4, 6, 8, 12, 24
Factors of 28 are; 1, 2, 4, 7, 14, 28
The highest greatest common factor is 4.
Now, 4 × 6 gives 24
While 4 × 7 gives 28.
Thus, our original equation is now;
4(6 + 7)
Using distributive property, let's add the number in the bracket first to get;
4(13).
Now,we multiply out to get 52.
Answer:4(7+6)
Step-by-step explanation: i passed the quiz with an 100%
A jewelry store sells necklaces in lengths that vary from 16 inches to 22 inches. Any necklaces outside of this criteria are rejected by the store’s buyers and will not be offered for sale in the store. Write an equation representing the minimum and maximum necklace lengths sold by the jewelry store.
Answer:
16-22
Step-by-step explanation:
Answer:
i agree with the other person
Step-by-step explanation:
PLEASE HELP ASAP
IT AN EMERGENCY
We're given two pairs of congruent sides, and a pair of congruent angles. The angles are not between the two congruent sides. So we don't have enough information to know if the triangles are congruent or not. SSA is not a valid congruence theorem. This is because there are some cases where two triangles are possible leading to ambiguity.
If the marked angles were between the tickmarked sides, then we could use SAS.
How many 1-inch cubes fill one row of the carton?
Answer: 5 because it has 5 space left
Answer:
5
Step-by-step explanation:
i did this on i-ready and got it right Good luck!
Which is true 0.45>0.5
0.45<0.5
4.05=0.45
4.05 <0.45
Answer:
4.05 is greater than 0.45
A random sample drawn from a population with mean μ= 66 and standard deviation σ= 6.
Required:
a. Comment on the sampling distribution of the sample mean with n = 16 and n = 36.
b. Can you use standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 for both sample sizes?
c. Report the probability if you answered yes to the previous question for either sample size.
Answer:
In step by step explanation
Step-by-step explanation:
a) Normal distribution N( 0, 1 )
If the sample size is equal n = 16 we have to use t-student distribution since n < 30.
In the case n = 36 we should use normal distribution (z tables)
b) We can´t use the standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 in the first case n < 30 .
We can calculate that probability in the case of the second sample