Answer:
31
Step-by-step explanation:
Let the smallest integer be x.
Since the 4 integers are consecutive (they come right after the other),
2nd integer= x +1
3rd integer= x +1 +1= x +2
4th integer= x +2 +1= x +3
Sum of the integers= 122
x +x +1 +x +2 +x +3= 122
4x +6= 122
4x= 122 -6
4x= 116
x= 116 ÷4
x= 29
3rd number
= 29 +2
= 31
It rains 1 day in a week and dry for 6 days. What fraction of the week is dry
Answer:
6/7
Step-by-step explanation:
7 days make a week. 7 would go into the denominator and 6 would go in the numerator. 6 is the amount of days through the week that it is dry.
Answer:
6/7
Step-by-step explanation:
[tex]\frac{number \ of \ dry \ days}{total \ number \ of \ days \ in \ a \ week} =\frac{6}{7}[/tex]
Which angle is an alternate exterior angle to 28?
3
0 23
0 24
2
3
4
* 25
t
8
5
7 6
026
Dong
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Answer:
∠4
Step-by-step explanation:
"Alternate" means the angle is on the other side of the transversal t. "Exterior" means it is on the outside of line e crossing the transversal. The alternate exterior angle to angle 8 is angle 4.
Think of 5 positive integers that have a mean, median, mode, and range of 6.
Joyce paid $60.00 for an item at the store that was 50 percent off the original price. What was the original price?
$
Give your answer to the nearest cent.
Find the area of the surface generated when the given curve is revolved about the y-axis. The part of the curve y=4x-1 between the points (1, 3) and (4, 15)
Answer:
Step-by-step explanation:
Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.
Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1
4x = y + 1
[tex]x = \dfrac{y+1}{4}[/tex]
[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]
By integration, the required surface area in the revolve is:
[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]
where;
g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]
∴
[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]
[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]
[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]
[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]
Draw a triangle ABC, where AB = 8 cm , BC = 6 cm and angle B=70^ and locate its circumcentre and draw the circumcircle.
Step-by-step explanation:
ΔABC, where AB = 8 cm, BC = 6 cm, B = 70° Construction: (i) Draw the ∆ABC with the given measurements. (ii) Construct the perpendicular bisector at any two sides (AB and BC) and let them meet at S which is the circumcircle. (iii) S as centre and SA = SB = SC as radius, draw the circumcircle to pass through A, B, and C. Circum radius = 4.3cm .draw-triangle-abc-where-cm-bc-and-70-and-locate-its-circumcentre-and-draw-the-circumcircle
Need helpppppppppppppppppp
Answer:
-18
Step-by-step explanation:
B=-6 C=2 P.E.M.D.A.S.
b - 6(c)
-6 - 6(2)
-6 - 12 . The negatives cancel out, adding each other
-6 + -12
= -18 :)
Answer:
b - 6c
= -6 - 6x2
= -6 x( 1+2)
= -6x3
= -18
Congruent sides???????????
Answer:
the second option : ST and WX
Step-by-step explanation:
congruent means they would completely cover each other when oriented in the same direction and positioned at the same location.
after dying the two mirroring actions we get
VS correlates to ZW
ST correlates to WX
TU correlates to XY
UV correlates to ZY
angle 1 is congruent to angle 2 prove p is parallel to q
You'll need 2 more lines to complete this two column proof.
---------------------
Line 4
For the "statement" portion, you'll say something like [tex]\angle 2 \cong \angle 3[/tex]
The reason for this statement is "transitive property"
We're basically combining lines 1 and 3 to form this new line.
The transitive property is the idea that if A = B and B = C, then A = C. We connect the statements like a chain.
---------------------
Line 5
The statement is what you want to prove since this is the last line.
So the statement is [tex]p || q[/tex]
The reason is "converse of corresponding angles theorem"
As you can probably guess, this theorem says "If two corresponding angles are congruent, then the lines are parallel".
convert 1.5% to decimal and a fraction. Show and explain your method
Answer:
0.015 and 3/200.
Step-by-step explanation:
1.5% is equal to 0.015. Percents are always equal to their decimal counterparts; basically, the number over 100. Dividing 1.5 by 100 will yield us 0.015.
0.015 is going to be equal to 15/1000, or 3/200. Since we did 1.5/100, we need to multiply both sides of the fraction by 10 so there are no decimal points. Therefore, this is 15/1000. If we divide both sides of this fraction by 5, then we get 3/200, which is the most simplified form.
A local pizza place claims that they average a delivery time of 6.46 minutes. To test this claim, you order 10 pizzas over the next month at random times on random days of the week. You calculate that the average delivery time is 8.56 minutes with a standard deviation of 1.068 minutes. You create a 90% confidence interval of (7.941, 9.179). Of those listed below, what is the best conclusion you can make?
1) We cannot determine the proper interpretation based on the information given.
2) You are 90% confident that the average delivery time is less than 6.46 minutes.
3) The average delivery time does not significalty differ from 6.46 minutes.
4) The percentage of pizzas that arrive around 6.46 minutes is 90%.
5) You are 90% confident that the average delivery time is greater than 6.46 minutes.
Answer:
Place the event
But he sobered down when he saw that Jimmy was wounded.
Jimmy comes
up with the plan of curing the Emperor by telling him to eat watermelon.
The Emperor fa
lls sick with dysentery, which has plagued the kingdom.
The Emperor is cured after eating a few slices of fresh watermelon.
The next day, the page asks the Emperor t
o consume a slice of watermelon as a cure.
↓
↓
Reset Submit
Step-by-step explanation:
Write the equation of the line with the given conditions. passing through (-1, -7) and perpendicular to the line with equation 4x + 5y = 31
Answer:
y = 5/4 x - 23/4
Step-by-step explanation:
4x + 5y = 31
5y = - 4x +31
y = -4/5 x + 31/5
⊥ slope = 5/4
-7 = 5/4 (-1) + B
-28 = -5 + 4b
-23 = 4B
b = -23/4
Find the radius of the circle if the center is at (1, 2) and the point (-5, 6) lies on the circle.
On a coordinate plane, a circle has center point (1, 2). A point on the circle is at (negative 5, 6).
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Answer:
2√13
Step-by-step explanation:
The distance between the center of the circle and a point on the circle is the radius. That distance is given by the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
d = √((-5 -1)² +(6 -2)²) = √(36 +16) = √52
d = 2√13
The radius of the circle is 2√13.
Two factors of x² +5x+6 are ….. and …..
Hello!
[tex]\large\boxed{(x + 2)(x + 3)}[/tex]
x² + 5x + 6
Find two numbers that add up to 5 and multiply to 6. We get:
2, 3
Therefore:
(x + 2)(x + 3)
Need answers asap!!!!!!!!!!!!!!
Answer:
The answer is
x equal -243
Answer:
-243 is yr correct answer.
Step-by-step explanation:
(-3)^-5=1/x1/(-3)^5=1/x1/-243=1/xx= -243hope it helps
stay safe healthy and happy...Can someone solve this for me and a couple more questions ?
Answer:
C. -4
Step-by-step explanation:
Answer:
(c) - 4
is your right answer
At a hockey game, a vender sold a combined total of 228 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
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Answer:
152 sodas76 hot dogsStep-by-step explanation:
Of the items sold, sodas were 2/(2+1) = 2/3 of the total.
(2/3)(228) = 152 . . . sodas were sold
152/2 = 76 . . . . hot dogs were sold
A manufacturer inspects a sample of 500 smart phones and finds that 496 of them have no defects. The manufacturer sent a shipment of 2000 smartphones to a distributor. Predict the number of smartphones in the shipment that are likely to have no dects.
Answer:
1984
Step-by-step explanation:
How much do I need to subtract from 67/10 to make 6
Answer:
0.7
Step-by-step explanation:
67/10 is the same as 6.7 when you subtract the 0.7 you will remain with 6
A retired couple has up to $50,000 to invest. As their financial adviser, you recommend that they place at least $35,000 in Treasury bills yielding 1% and at most $10,000 in corporate bonds yielding 3%. Write and graph the system of equations of linear inequalities that describes the possible amounts of each investment.
Answer:
See Explanation
Step-by-step explanation:
According to the Question,
Given that, A retired couple has up to $50,000 to invest. As their financial adviser, you recommend that they place at least $35,000 in Treasury bills yielding 1% and at most $10,000 in corporate bonds yielding 3%.
Therefore,
Let, x be the amount of money invested in Treasury bills
y be the amount invested in corporate bonds
Thus, the system of equations of linear inequalities is
x + y ≤ 50000
x ≥ 35000
0 ≤ y ≤ 10000
For, the graph of the system of equations of linear inequalities describes the possible amounts of each investment.
(Please find in the attachment)
PLEASE HELP !!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
It is A and B
Step-by-step explanation:
!!!!Plzzz help!!!!
For your initial post: Discuss your strategy for
establishing identities. Why do you think it is
usually preferable to start with the side
containing the more complicated expression
when establishing an identity?
Answer:
Yes it is very good for establishing identities.
Step-by-step explanation:
Since its a very preferable start it is a very good way to establish identity.
Tell whether the following two triangles can be
proven congruent through SAS.
A.Yes, the two triangles are congruent
because two sides and their included
angle are congruent in both triangles.
B.No, the two triangles don't have
corresponding sides marked congruent.
C. Yes, the two triangles are congruent because they’re both right triangles.
D.No, the two triangles can only be proven congruent through SSA.
Answer:
B. No, the two triangles don't have
corresponding sides marked congruent.
please i need help with this rn
Hi there!
[tex]\large\boxed{f(9) = 12}[/tex]
Evaluating f(x) at x = 9 means we must use the piecewise function where x = 9 is included.
f(x) = 12 includes 9 because a "≤" is inclusive of the interval. Thus:
f(9) = 12
In order to win a prize, Heather randomly draws two balls from a basket of 40. There are 25 blue balls, and the rest are green balls. Of the blue balls, 12% are winning balls. Of the green balls, 20% are winning balls. Calculate the expected number of winning balls that Heather draws.
Answer:
The expected number of winning balls that Heather draws is 0.3.
Step-by-step explanation:
The balls are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Expected value of the hypergeometric distribution:
The expected value is given by:
[tex]E(X) = \frac{nk}{N}[/tex]
Expected number of blue and green balls:
40 balls, which means that [tex]N = 40[/tex]
2 are chosen, which means that [tex]n = 2[/tex]
25 are blue, which means that [tex]k = 25[/tex]
So
[tex]E(X) = \frac{nk}{N} = \frac{25(2)}{40} = 1.25[/tex]
1.25 balls are expected to be blue and 2 - 1.25 = 0.75 green.
Of the blue balls, 12% are winning.
Of the green balls, 20% are winning.
Calculate the expected number of winning balls that Heather draws.
[tex]E_w = 1.25*0.12 + 0.75*0.2 = 0.3[/tex]
The expected number of winning balls that Heather draws is 0.3.
An electronic system contains three cooling components that operate independently. The probability of each component's failure is 0.05. The system will overheat if and only if at least two components fail. Calculate the probability that the system will overheat.
Answer:
[tex]Pr= 0.00725[/tex]
Step-by-step explanation:
Given
[tex]p = 0.05[/tex] ---- probability that each component fails
[tex]n = 3[/tex]
Required
[tex]P(System\ Overheats)[/tex]
We understand that the system will overheat if at least 2 component fails; Assume the components are: x, y and z
The events that the system will overheat are: xyz', xy'z, x'yz and xyz
Where ' means that the component did not fail, and the probability is 1 - p (i.e. complement rule)
So, we have:
[tex]xyz' \to 0.05 * 0.05 * (1 - 0.05) = 0.002375[/tex]
[tex]xy'z \to 0.05 * (1 - 0.05)* 0.05 = 0.002375[/tex]
[tex]x'yz \to (1 - 0.05)* 0.05 * 0.05 = 0.002375[/tex]
[tex]xyz \to 0.05 * 0.05 * 0.05 =0.000125[/tex]
So, the required probability is:
[tex]Pr= 0.002375 +0.002375 +0.002375 + 0.000125[/tex]
[tex]Pr= 0.00725[/tex]
How can you use transformations to graph this function?
Answer:
What function?
Step-by-step explanation:
Express 20% as a decimal number
Answer: 0.2
Step-by-step explanation: 20/100=1/5
and 1/5 equals 1 divided by five so it is 0.2
The average defect rate on a 2010 Volkswagen vehicle was reported to be 1.33 defects per vehicle. Suppose that we inspect 100 Volkswagen vehicles at random. (a) What is the approximate probability of finding at least 157 defects
Answer:
0.0207 = 2.07% approximate probability of finding at least 157 defects
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
n instances of a Poisson distribution can be approximated to a normal distribution, with [tex]\mu = n\lambda, \sigma = \sqrt{\lambda}\sqrt{n}[/tex]
The average defect rate on a 2010 Volkswagen vehicle was reported to be 1.33 defects per vehicle.
This means that [tex]\lambda = 1.33[/tex]
Suppose that we inspect 100 Volkswagen vehicles at random.
This means that [tex]n = 100[/tex]
Mean and standard deviation:
[tex]\mu = n\lambda = 100*1.33 = 133[/tex]
[tex]\sigma = \sqrt{\lambda}\sqrt{n} = \sqrt{1.33}\sqrt{100} = 11.53[/tex]
What is the approximate probability of finding at least 157 defects?
Using continuity correction(Poisson is a discrete distribution, normal continuous), this is [tex]P(X \geq 157 - 0.5) = P(X \geq 156.5)[/tex], which is 1 subtracted by the p-value of Z when X = 156.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{156.5 - 133}{11.53}[/tex]
[tex]Z = 2.04[/tex]
[tex]Z = 2.04[/tex] has a p-value of 0.9793.
1 - 0.9793 = 0.0207
0.0207 = 2.07% approximate probability of finding at least 157 defects
prove that
[tex]2 \tan30 \div 1 + tan ^{2} 30 = sin60[/tex]
prove that
.
Step-by-step explanation:
2tan 30° / 1 + tan² 30° =
2(⅓√3) /1 + (⅓√3)² =
⅔√3 / 1+ ⅓ =
⅔√3 / 4/3 =
2/4 √3 =
½√3 = sin 60° (proven)