Answer:
6, -6, 6, -6 and 6.
Step-by-step explanation:
Given the recursion formula for a sequence
[tex]a_{n+1}=-a_n\\$where a_1=6\\[/tex]
The first five terms of the sequence are:
[tex]\text{First Term, }a_1=6\\$Second Term, a_2=a_{1+1}=-a_1=-6\\$Third term, a_3=a_{2+1}=-a_2=6\\$Fourth term, a_4=a_{3+1}=-a_3=-6\\$Fifth term, a_5=a_{4+1}=-a_4=6[/tex]
Therefore, the first five terms of the sequence:
[tex]a_1,a_2,a_3,a_4,a_5=6, -6, 6, -6$ and 6.[/tex]
what is the area of a circle with a diameter of 8
Step-by-step explanation:
Radius (R) =diameter /2 =8/2 =4
So area=
[tex]\pir {r}^{2} = \pi {4}^{2} = 50.27[/tex]
Hope this helps..
how and explain how to find the value of x . step by step I will give the most correct one the brainiest
Answer:
X=96
Step-by-step explanation:
180-134=46
180-130=50
SUM OF TWO INTERIOR ANGLES = EXTERIOR ANGLE
50 + 46=96
Ashley mixes two types of soft drinks with different types of concentration: one soft drink has 20% sugar and the other drink has 45% sugar. Each can has 250 milliliters of soda. What is the sugar concentration of the mixed soft drink?
Answer:
Sugar concentration of the mixed soft drink will be 32.5%.
Step-by-step explanation:
Sugar concentration of first drink = 20%
Volume of first soda = 250 ml
Sugar in first soda = 20% of 250 ...... (1)
Sugar concentration of second drink = 45%
Volume of second soda = 250 ml
Sugar in second soda = 45% of 250 ...... (2)
Let [tex]x\%[/tex] be the sugar concentration in resultant mixture.
Volume of mixture = 250 + 250 = 500 ml
Sugar in mixture = [tex]x\%[/tex] of 500 ml ...... (3)
Total sugar concentration (Adding (1) and (2)) and equating it to equation (3):
20% of 250 + 45% of 250 = [tex]x\%[/tex] of 500
[tex]\Rightarrow \dfrac{20}{100} \times 250 + \dfrac{45}{100} \times 250 = \dfrac{x}{100} \times 500\\\Rightarrow 2 \times x = 65\\\Rightarrow x = 32.5\%[/tex]
Hence, Sugar concentration of the mixed soft drink will be 32.5%.
arc
An 8 inch pie (diameter is 8) was sliced into 4 equal parts. How large is the 2 points
pie crust of one slice? *
Answer:
6.28 inches
Step-by-step explanation:
Given that the diameter of the pie=8 inch
Radius=Diameter/2
Therefore: Radius of the pie=8/2=4 Inch
Circumference of a circle [tex]=2\pi r[/tex]
Since the pie is sliced into 4 equal parts:
Length of the Pie crust of one slice[tex]=\dfrac{2\pi r}{4}[/tex]
Substituting the value of r, we obtain:
Length of the Pie crust of one slice[tex]=\dfrac{2*\pi *4}{4}\\=2\pi $ inches\\=6.28 inches (correct to 2 decimal places)[/tex]
A parabola can be drawn given a focus of (5, 10) and a directrix of y= -2. what can be said about the parabola?
the parabola has a vertex at (_,_), has a low-value of _ and it opens __.
Answer:
(5, 4)4upwardStep-by-step explanation:
The directrix is a horizontal line (y=-2). The parabola will open in the direction the focus is from the directrix. Here, the y-coordinate of the focus is 10, so the focus is above the directrix and the parabola opens upward.
The vertex is halfway between the directrix and the focus, so has y-coordinate ...
(-2 +10)/2 = 4
Since the parabola opens upward, the vertex is a minimum (the "low value"). Its x-coordinate is the same as that of the focus, so the vertex is (5, 4).
The parabola has a vertex at (5, 4), has a low value of 4, and it opens upward.
In circle O two secants,
ABP and CDP, are drawn to external point P. If mAC = 72°, and mBD = 34°, what is the measure of ∠P?
(1) 19° (3) 53°
(2) 38° (4) 106°
Answer:
(1)19°
Step-by-step explanation:
The diagram is drawn and attached below.
Let x=mAC = 72°; and
y=mBD = 34°
By the Angle-Arc relationship, the external angle is half the difference.
[tex]\angle P=\frac{1}{2}(x^\circ-y ^\circ)\\$Therefore:\\m\angle P=\frac{1}{2}(72^\circ-34 ^\circ)\\m\angle P=19^\circ[/tex]
Type the expression that results from the following series of steps:
Start with t times by 5.
Answer:
t times 5 is t * 5 or 5t.
The art teacher needs 70 markers for her classes. The markers come in packages of 15. How many packages of markers will the art teacher need to buy?
Answer:
5
Step-by-step explanation:
Take the number of markers and divide by the number in each package
70/15
4.6666repeating
Round to the nearest whole number to determine the number of packages
5
They will need to buy 5 packages
Activity Question 1 When designing a truss, a truss builder might know the base angle measurement and the length of the tie beam needed. The next step is to compute the height of the king post. Let's take a look at some right triangles to see whether knowing the measure of an acute angle of a right triangle and the length of one of the sides is enough to find the lengths of the other two sides. Part A What is the measure of ∠BAC?
Answer:
36.87°
Step-by-step explanation:
Assume the triangles are as in the diagram below.
∠BAC includes ∠DAE.
The measure of ∠BAE is 36.87°.
Answer:
36.87°
Step-by-step explanation:
i just had this question on edmentum and it was right.
find the pattern then find the next term of the sequence. 5, 1, 7, 0, 9, -1, 11
Answer:
5, 1, 7, 0, 9, -1, 11, -2, 13
Step-by-step explanation:
5, 1, 7, 0, 9, -1, 11
Two series in one:
5, 7, 9, 11, 131, 0, -1, -2What is the most important difference between an experiment and an observational study? An experiment is conducted in a laboratory and an observational study is conducted outside. An experiment has a treated group and a control group while an observational study does not. In an experiment, the researcher applies a treatment to a randomly assigned group and studies the results, while an observational study just looks at things that have happened without intervention. In an experiment, the researcher studies the effects of medical treatments or other scientific results, while an observational study looks at subjects in the social science arena.
Answer:
In an observational study, we measure or survey members of a sample without trying to affect them. In a controlled experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.
hope it helps :)
mark as brainliest
In an experiment, the researcher applies a treatment to a randomly assigned group and studies the results, while an observational study just looks at things that have happened without intervention.
What is an experiment?An experiment is designed to test the effect of an intervention or treatment on a particular outcome, by comparing the results from a group that receives the intervention to a control group that does not receive the intervention. In this way, the experiment can establish cause-and-effect relationships and determine if the treatment has a significant effect.
On the other hand, an observational study does not involve any manipulation of the independent variable. It simply observes and records the relationship between variables. Observational studies cannot establish cause-and-effect relationships and the results may be subject to confounding variables, which can make it difficult to interpret the findings.
Hence, the correct answer would be an option (C).
Learn more about the experiment here:
https://brainly.com/question/17314369
#SPJ6
Nicole has x beads. Together we have 56 beads. How many beads will I have if I lose 1/4 of my beads?
Answer:
(56 - x) * 3/4
Step-by-step explanation:
x + y = 56
y = 56 - x
y' = (56 - x) * 3/4
You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37. A random sample of 780 men over the age of 50 found that 206 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim. Test the relevant hypotheses using a 10% level of significance. Give answers to at least 4 decimal places. What are the correct hypotheses?
Answer:
1. Yes, the sample data provides convincing evidence to support the claim that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37
2. The correct hypotheses are;
The null hypothesis is H₀: p ≥ p₀
The alternative hypothesis is Hₐ: p < p₀
Step-by-step explanation:
given
The null hypothesis is H₀: p ≥ p₀ where p₀ = 0.37
The alternative hypothesis is Hₐ: p < p₀
The formula for the z test is presented as follows;
[tex]z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0 (1 - p_0)}{n}}}[/tex]
Where:
[tex]\hat p[/tex] = Sample proportion = 206/780 = 0.264
p₀ = Population proportion = 0.37
n = Sample size = 780
α = Significance level = 10% = 0.01
Plugging in the values, we have;
[tex]z=\dfrac{0.264-0.37}{\sqrt{\dfrac{0.37 (1 - 0.37)}{780}}} = -6.13[/tex]
From the the z relation/computation, we have the p value = 0.000000000451
Since the p value which is 0.000000000451 is less than α, which is 0.01 we reject the null hypothesis and we fail to reject the alternative hypothesis, that is there is sufficient statistical evidence to suggest that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37.
What is the coefficient of the term x5y7 in the expansion of (x - y)12 ?
Answer:
12 and -12
Step-by-step explanation:
12x-12y is the expansion using the distributive property, so the coefficient of x is 12 and the coefficient of y is -12
Find m
A) 110
B) 222
C) 28
D) 82
Answer:
As angel WVU = angel WVF + angel FVU
Therefore angel WVF =152 - 70
so, angel WVF = 82
The National Cancer Institute estimates that 3.65% of women in their 60s get breast cancer. A mammogram can typically identify correctly 85% of cancer cases and 95% of cases without cancer. What is the probability that a woman in her 60s who has a positive test actually has breast cancer?
Answer:
39.17% probability that a woman in her 60s who has a positive test actually has breast cancer
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Positive test.
Event B: Having breast cancer.
3.65% of women in their 60s get breast cancer
This means that [tex]P(B) = 0.0365[/tex]
A mammogram can typically identify correctly 85% of cancer cases
This means that [tex]P(A|B) = 0.85[/tex]
Probability of a positive test.
85% of 3.65% and 100-95 = 5% of 100-3.65 = 96.35%. So
[tex]P(A) = 0.85*0.0365 + 0.05*0.9635 = 0.0792[/tex]
What is the probability that a woman in her 60s who has a positive test actually has breast cancer?
[tex]P(B|A) = \frac{0.0365*0.85}{0.0792} = 0.3917[/tex]
39.17% probability that a woman in her 60s who has a positive test actually has breast cancer
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
C. [tex](f+g)(x)=-5^x-3x-6[/tex]
Step-by-step explanation:
→Set it up, like so:
[tex](-5^x-4)+(-3x-2)[/tex]
[tex]-5^x-4-3x-2[/tex]
→Add like terms (-4 and -2):
[tex]-5^x-3x-6[/tex]
The product of two consecutive positive integers is 132. What are the integers?
Answer:
The integers are 11 and 12
Step-by-step explanation:
11 and 12 are consecutive positive integers, and 11 x 12 = 132.
What are the answers to a b and c ?
In a survey of first graders, their mean height was 49.9 inches with a standard deviation of 3.15 inches. Assuming the heights are normally distributed, what height represents the first quartile of these students?
Answer:
Height = 47.77 inches
Step-by-step explanation:
We are given;
Mean = 49.9 in
Standard deviation;SD = 3.15 in
The first quartile is the 25th percentile, which means it's where 25% of the data falls.
Now from the normal distribution table attached, we can see that the z-value for 25% or 0.25 is approximately
-0.675.
To find the height that represents the first quartile of these students, we will use the formula;
z = (height - mean)/(SD)
Making height the subject ;
height = (z × SD) + mean
Plugging in the relevant values to obtain;
Height = (-0.675 × 3.15) + 49.9
Height ≈ 47.77 inches
The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 24 minutes and a standard deviation of 7 minutes. Find the probability that a randomly selected athlete uses a stairclimber for
(a) less than 19 minutes,
(b) between 24 and 33 minutes, and
(c) more than 40 minutes.
Which event is unusual?
Answer:
(a) The probability that a randomly selected athlete uses a stairclimber for less than 19 minutes is 0.2388.
(b) The probability that a randomly selected athlete uses a stairclimber for between 24 and 33 minutes is 0.3997.
(c) The probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is 0.0113.
Step-by-step explanation:
We are given that the amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 24 minutes and a standard deviation of 7 minutes.
Let X = amounts of time per workout an athlete uses a stairclimber
So, X ~ Normal([tex]\mu=24,\sigma^{2} =7^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time = 24 minutes
[tex]\sigma[/tex] = standard deviation = 7 minutes
(a) The probability that a randomly selected athlete uses a stairclimber for less than 19 minutes is given by P(X < 19 minutes)
P(X < 19 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{19-24}{7}[/tex] ) = P(Z < -0.71) = 1 - P(Z [tex]\leq[/tex] 0.71)
= 1 - 0.7612 = 0.2388
The above probability is calculated by looking at the value of x = 0.71 in the z table which has an area of 0.7612.
(b) The probability that a randomly selected athlete uses a stairclimber for between 24 and 33 minutes is given by = P(24 min < X < 33 min)
P(24 min < X < 33 min) = P(X < 33 min) - P(X [tex]\leq[/tex] 24 min)
P(X < 33 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{33-24}{7}[/tex] ) = P(Z < 1.28) = 0.8997
P(X [tex]\leq[/tex] 24 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{24-24}{7}[/tex] ) = P(Z [tex]\leq[/tex] 0) = 0.50
The above probability is calculated by looking at the value of x = 1.28 and x = 0 in the z table which has an area of 0.8997 and 0.50 respectively.
Therefore, P(24 min < X < 33 min) = 0.8997 - 0.50 = 0.3997
(c) The probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is given by P(X > 40 minutes)
P(X > 40 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{40-24}{7}[/tex] ) = P(Z > 2.28) = 1 - P(Z [tex]\leq[/tex] 2.28)
= 1 - 0.9887 = 0.0113
The above probability is calculated by looking at the value of x = 2.28 in the z table which has an area of 0.9887.
The event of probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is unusual because this probability is less than 5% and any even whose probability is less than 5% is said to be unusual.
2. Find the measure of angle G. Round your answer to the nearest degree.
Answer:
G = 53 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin G = 24/30
Take the inverse sin of each side
sin ^-1 sin G = sin ^-1 (24/30)
G =53.13010235
To the nearest degree
G = 53 degrees
During a trip, Amy had to take two different trains. Her first train traveled for 3 hours, and the second
train traveled for 4 hours. Combined, the trains traveled 625 miles.
If the equation 3m + 4n = 625 represents this situation, which statements are true regarding this
equation?
Select two that apply.
The variable m in the equation represents the speed of the first train.
The variable m in the equation represents the speed of the second train.
The variable n in the equation represents the speed of the second train.
The variable n in the equation represents the speed of the first train.
The variable m in the equation represents the number of hours Amy traveled on the
first train.
The variable n in the equation represents the number of hours Amy traveled on the
second train.
Answer:
Let's solve for m.
3m + 4n = 625
Step 1: Add -4n to both sides.
3m + 4n + −4n = 625 + −4n
3m = −4n + 625
Step 2: Divide both sides by 3.
3m/3 = 4n + 625/3
m = -4/3 n + 625/3
C) The variable m in the equation represents the number of hours Amy traveled on the
first train.
D) The variable n in the equation represents the number of hours Amy traveled on the
second train.
Marcia's wages are £260 per week.
She wants to save some money to buy a computer.
The computer costs £218.
Marcia is going to save 5% of her wages each week.
How many weeks will it take her to save enough money to buy the computer?
Answer:
17 weeks
Step-by-step explanation:
Please refer to the picture attached.
At the end of each week, she will be able to save 13 dollars. I'm the 17th week, whe will save more than 218 dollars and will be able to afford to buy the computer.
However, in 16th week, she will only save 208 dollars which is insufficient to buy the laptop.
Hence, u round up the value of x in order to get the answer.
If x^6=60 and w^10=20, what is x^12×w^-10? A. 36, B. 60, C. 180 or D. 360
Answer:
[tex] x^{12} w^{-10}[/tex]
And we can find this rewriting the expression in terms of the info given and we got:
[tex]x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}[/tex]
And replacing we got:
[tex]x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180[/tex]
And the best option would be:
C. 180
Step-by-step explanation:
For this case we know that:
[tex] x^6, w^{10} = 20[/tex]
And we want to find the value for:
[tex] x^{12} w^{-10}[/tex]
And we can find this rewriting the expression in terms of the info given and we got:
[tex]x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}[/tex]
And replacing we got:
[tex]x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180[/tex]
And the best option would be:
C. 180
You've found yourself trapped in a desert, desperate for a drink of water. Amazingly, you come across a food cart right there and they have glasses of water available for just $1! You even have a dollar! You're all set. Except the cart vendor tells you He only sells 80z glasses of water, and he only have 6oz and 10oz glasses. "I'll pay a dollar for the 6oz!" you say. "No," he replies, "I won't be cheating you." How can you use the 6oz glass and the 10oz glass to measure out exactly 8oz?
If I'm understanding the problem correctly, the vendor sells water in exactly 8 oz increments, but only has glasses that can hold 6 oz or 10 oz.
Fill up the 10 oz glass, then (carefully) pour its contents into a 6 oz glass until it it is full. Then the 10 oz glass should contain 4 oz of water. Drink the 4 oz, repeat this process to get your 8 oz, and pay the man.
BC =
Round your answer to the nearest hundredth.
B
35°
6
А
Using the cosine ratio, the length of BC to the nearest hundredth is: 4.91.
What is the Cosine Ratio?Cosine ratio is: cos ∅ = adjacent side/hypotenuse
Given the right triangle in the diagram above, thus:
∅ = 35°Adjacent = ? = BCHypotenuse = 6Thus:
cos 35 = BC/6
BC = cos 35 × 6
BC = 4.91
Thus, using the cosine ratio, the length of BC to the nearest hundredth is: 4.91.
Learn more about cosine ratio on:
https://brainly.com/question/15793827
This question is rlly confusing
Answer: C.
Step-by-step explanation:
To find the discounted value off of a full price, you can multiply the full price by the discount percentage to find the discount:
250 * 0.20 = 50
The discount is 50 dollars.
The laptop costs $250, but with the discount of $50, it is now for sale for $200.
The correct answer is C.
Simplify the following expression.
(2x + 5) + (3x2 + 7x + 3)
Answer:
3x^2 + 9x + 8
Step-by-step explanation:
2x+5+3x^2+7x+3
2x+5+3x^2+7x+3
(3x^2)+(2x+7x)+ (5+3)
3x^2+9x+8
Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is gbb, then R9gbb)=1. Suppose that the random variable X is defined in terms of R as follows: X=2R^2-4R-2. The values of X are thus:
Complete Question
The complete question is shown on the first uploaded image
Answer:
Value x of X -3 -7 -15
[tex]P_X (x)[/tex] [tex]\frac{1}{2}[/tex] [tex]\frac{3}{8}[/tex] [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
From the question we are told that
The values of X are [tex]X = -3 , -7 , -15[/tex]
The total number of outcomes is n = 8
The probability distribution function of X is evaluated as follow
[tex]p(X = -3 ) = \frac{N_{-3}}{n}[/tex]
Where [tex]N{-3}[/tex] is the number of time X = -3 occurred and from the table the value is [tex]N _{-3} = 4[/tex]
Therefore
[tex]p(X = -3 ) = \frac{4}{8}[/tex]
[tex]p(X = -3 ) = \frac{1}{2}[/tex]
Now
[tex]p(X = -7 ) = \frac{N_{-7}}{n}[/tex]
Where [tex]N_{-7} = 3[/tex] from table
So
[tex]p(X = -7 ) = \frac{3}{8}[/tex]
Also
[tex]p(X = -15 ) = \frac{N_{-15}}{n}[/tex]
[tex]p(X = -15 ) = \frac{1}{8}[/tex]
