Answer:
Step-by-step explanation:
Because 48 and 89 have the same sign, that is, the negative sign, their sum takes on that sign:
-48
-89
---------
-137
Eggs ares sold in boxes. A small box holds 6 eggs hina buys x small boxes of eggs write down in terms of x the total number of eggs in these small boxes
[tex]6x[/tex]
............................................
what is the y intercept for f(x) = 5x +7
Answer:
7
Step-by-step explanation:
the slope intercept form is y=mx + b
where b is the y intercept,
and your question is y=5x + 7
so the y intercept form would equal to 7
What is the measure of x? Help me on this Geometry question.
Answer:
21°
Step-by-step explanation:
the angles of triangle abc has to = 180 so subtract the known angles to get 21
angles bca and daf have to be the same so its 21
Answer:
[tex]x=21[/tex]
Step-by-step explanation:
We have been given an image of two parallel lines cut by a transversal. We are asked to find the measure of x.
We know that corresponding angles of two parallel lines are equal. We can see that angle BCA and angle DAF are corresponding angles.
Let us find measure of angle BCA using angle sum property.
[tex]54^{\circ}+105^{\circ}+m\angle BCA=180^{\circ}[/tex]
[tex]159^{\circ}+m\angle BCA=180^{\circ}[/tex]
[tex]159^{\circ}-159^{\circ}+m\angle BCA=180^{\circ}-159^{\circ}[/tex]
[tex]m\angle BCA=21^{\circ}[/tex]
Therefore, the value of x is 21 degrees.
You buy a rental property for $180,000. Assuming that you could sell the property for $250,000 at the end of 6 years, what is your return based on the following cash flows? Year 0 (now) = – 180,000 End of Year 1 = + 24,000 End of Year 2 = + 24,000 End of Year 3 = – 3,000 and +12,000 End of Year 4 = + 18,000 End of Year 5 = + 30,000 End of Year 6 = + 32,000
Answer:
15.542%
Step-by-step explanation:
For uneven cash flows such as those in this problem, there is no formula for "internal rate of return" (IRR). It must be computed graphically or iteratively. Spreadsheets and financial calculators are equipped to do this calculation. Attached is the result of the calculation done by a graphing calculator.
The sum of "present value" of each of the cash flows is zero when the discount rate is the IRR.
When visiting his parents, Tyler drives at an average speed of 42 km/h through urban areas and at an average speed of 105 km/h on the motorway. His journey usually takes him 2.5 hours. One day when there is fog, he sets off 1 hour early and only manages to drive at an average speed of 28 km/h in the urban areas and 60 km/h on the motorway. He arrives 30 minutes late. What was the total distance that Tyler travelled?
Answer:
168 km
Step-by-step explanation:
Let x represent the distance Tyler drives at the slower speed, and let y represent the distance at the higher speed. Using time = distance/speed, we can write equations for the total travel time:
x/42 +y/105 = 2.5
x/28 +y/60 = 4.0 . . . . . 1.5 hours more than the usual 2.5 hours
Multiplying the first equation by 210, we have ...
5x +2y = 525
Multiplying the second equation by 420, we get ...
15x +7y = 1680
Subtracting 3 times the first of these equations from the second, we have ...
(15x +7y) -3(5x +2y) = (1680) -3(525)
y = 105
Putting this into the very first equation, we get ...
x/42 + 105/105 = 2.5
x/42 = 1.5 . . . . . . subtract 1
x = 63 . . . . . . . . .multiply by 42.
The total distance to Tyler's parents' house is ...
63 km + 105 km = 168 km
Tyler's total travel distance is approximately 168 km.
Calculating Total Distance Traveled
To determine the total distance Tyler traveled, let du be the distance through urban areas and dm be the distance on the motorway.
→ The total distance is:
[tex]D = d_u + d_m[/tex]
First, using the normal journey:
→ Urban Area:
Speed = 42 km/h
Time = [tex]t_u[/tex] / 42,
→ Motorway:
Speed = 105 km/h
Time = [tex]t_m[/tex] / 105,
→ Total time for normal journey:
→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]
We have:
→ [tex]d_u[/tex] = 42 * [tex]t_u[/tex]
→ [tex]d_m[/tex] = 105 * [tex]t_m[/tex]
When there is fog:
→ Urban Area:
Speed = 28 km/h
Time = [tex]t__uf}[/tex] / 28
→ Motorway:
Speed = 60 km/h
Time = [tex]t_{um[/tex] / 60
Total time for foggy journey:
→ [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60
Given that he leaves 1 hour early and arrives 30 minutes late, the total journey time in foggy conditions is:
→ 2.5+1+0.5=4 hours
Thus,
→ [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60 = 4
Solving the Equations
We now have two equations:
→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]
→ [tex]t_{uf}\ /\ 28\ + t_{mf} \ /\ 60 = 4 hours[/tex]
Let's solve these equations step-by-step.
First, let's multiply the first equation by 210 (the least common multiple of 42 and 105):
→ [tex]210(t_u/42 + t_m/105) = 210*2.5[/tex]
→ [tex]5t_u+2t_m=525[/tex] (eq. 1)
Next, let's multiply the second equation by 420 (the least common multiple of 28 and 60):
→ [tex]420( t_u/28+ t_m /60)=420*4[/tex]
→ [tex]15t_u +7t_m =1680[/tex] (eq. 2)
We now solve these two linear equations:
→ [tex]5t_u+2t_m=525[/tex]
→ [tex]15t_u +7t_m =1680[/tex]
First, let's solve Equation 1 for [tex]t_m[/tex] in terms of [tex]t_u[/tex]:
→ [tex]d_m=(525-5d_u)/2[/tex]
Substitute this expression into Equation 2:
→ [tex]15t_u+7((525-5d_u)/2)=1680[/tex]
Multiply through by 2 to clear the fraction:
→ [tex]30t_u +7(525-5t_u )=3360[/tex]
→ [tex]30t_u +3675-35t_u =3360[/tex]
→ [tex]-5t_ u +3675=3360[/tex]
→ [tex]-5t_u=3360-3675[/tex]
→ [tex]-5t _u=-315[/tex]
→ [tex]t_u=63[/tex]
Now substitute [tex]t_u=63[/tex] back into Equation 1 to find [tex]t_m[/tex]:
→ [tex]5(63)+2t_m =525[/tex]
→ [tex]315+2t_m =525[/tex]
→ [tex]2t_m =210[/tex]
→ [tex]t_m=105[/tex]
Thus, the total distance Tyler travels is:
[tex]= t _u +t_m[/tex]
[tex]=63+105[/tex]
[tex]=168\ kilometers[/tex]
HELP! ONLY IF YOU KNOW THE ANSWER
also this goes with the other question I asked
Write the standard equation of the conic section you chose with its center or vertex at the origin. Describe the graph.
Answer:
Attached
Step-by-step explanation:
The conic section you can chose is a parabola
A parabola is a curve where any point on the curve is equidistant from the focus and from a directrix
When you have the vertex and focus points, you can write the equation of the parabola then graph it on a graph tool to visualize the curve.
Assume the vertex is at (3,1) and focus is at (3,5), then you notice here the x-coordinate for vertex and focus is the same , to mean one is top of the other.
This is a regular vertical parabola the x part is squared.
Vertex and focus are 4 units apart. This is by checking the difference in values of y-axis of vertex and focus.This is your p
The equation of the parabola will be
(x-h)²=4p(y-k)
but p=4
(x-3)²=4(4)(y-1)
(x-3)²=16(y-1)
x²-6x+9=16y-16
x²-6x-16y+25=0-----------------equation of the parabola
It is a right-side up parabola
Answer:
I only know question number one; the answer is
A parabola is a curve where any point on the curve is equidistant from the focus and from a directrix.
Step-by-step explanation:
What is cos3phi= 1/2??? Please help and explain!
Answer:
[tex]\large\boxed{\Phi=\dfrac{\pi}{9}+\dfrac{2k\pi}{3}\ or\ \Phi=-\dfrac{\pi}{9}+\dfrac{2k\pi}{3}}[/tex]
Step-by-step explanation:
[tex]\cos3\Phi=\dfrac{1}{2}\qquad\text{substitute}\ 3\Phi=\theta\\\\\cos\theta=\dfrac{1}{2}\iff\theta=\dfrac{\pi}{3}+2k\pi\ or\ \theta=-\dfrac{\pi}{3}+2k\pi\qquad k\in\mathbb{Z}\\\\\text{We're going back to substitution:}\\\\3\Phi=\dfrac{\pi}{3}+2k\pi\ or\ 3\Phi=-\dfrac{\pi}{3}+2k\pi\qquad\text{divide both sides by 3}\\\\\Phi=\dfrac{\pi}{9}+\dfrac{2k\pi}{3}\ or\ \Phi=-\dfrac{\pi}{9}+\dfrac{2k\pi}{3}[/tex]
Choose a number between and that is a multiple 45 of and 95 . Write all the numbers that she could choose. If there is more than one number, separate them with commas.
Answer with explanation:
To find the common multiple of 45 and 95,we will find HCF of 45 and 95.
45=3 × 3× 5
95=5 × 19
⇒H CF(45,95)
=3 × 3×5×19
=855
→Common multiple of 45 and 95 =855
→There are infinite number of multiple of 855 which are 855, 1710, 2565,.....
You have not written between which two numbers.So, you should write multiple of 855 such that it is smaller than the greater number.
Can someone please help me with this math question
Answer:
C'(4,4)
Step-by-step explanation:
The dilation of quadrilateral ABCD over the origin by a scale factor of 2 has the rule
(x,y)→(2x,2y)
So,
A(-3,-1)→A'(-6,-2)B(-1,1)→B'(-2,2)C(2,2)→C'(4,4)D(3,-2)→D'(6,-4)Hence, the coordinates of the image point C' are (4,4) (see attached diagram for details)
Answer:
The coordinates of C' = (4,4)
Step-by-step explanation:
The coordinates of C can be found by looking at the graph,
Coordinates of C = (2,2)
ABCD is dilated by a factor of 2 to get A'B'C'D'.
So, the coordinates of C' will be found by multiplying the coordinates of C by 2.
C' = (2*2,2*2)
C' = (4,4)
So, The coordinates of C' = (4,4)
Select the correct answer from each drop-down menu.
Monica built a remote-controlled, toy airplane for a science project. To test the plane, she launched it from the top of a building. The plane traveled a horizontal distance of
50 feet before landing on the ground. A quadratic function which models the height of the plane, in feet, relative to the ground, at a horizontal distance of x feet from the building
is shown
200+
-8060-40
20
-50+
20 40 GO 80
*
100
Since the domain represents
interval [
the airplane while it was in the air, the values of the domain should be restricted to the
Resot
Answer:
a horizontal distance of x feet from the building[0, 50]Step-by-step explanation:
The problem statement tells you that x represents the horizontal distance in feet that the airplane is from the building. The domain is the set of useful values of x, which will be from 0 to 50 feet. Values of x less than 0 or more than 50 make no sense in this scenario.
The variable z is inversely proportional to x. When x is 6, z has the value of 2. What is the value of z when x=13
Round to at least the thousandths place if needed
Answer:
[tex]z=0.923[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and z, represent an inverse variation if it can be expressed in the form [tex]z*x=k[/tex] or [tex]z=k/x[/tex]
step 1
Find the value of k
For x=6, z=2
[tex]z*x=k[/tex]
substitute
[tex]2*6=k[/tex]
[tex]k=12[/tex]
therefore
The equation of the inverse variation is equal to
[tex]z*x=12[/tex]
step 2
What is the value of z when x=13
substitute the value of x in the equation and solve for z
[tex]z*(13)=12[/tex]
[tex]z=12/13[/tex]
[tex]z=0.923[/tex]
A box contains 13 transistors, 4 of which are defective. If 4 are selected at random, find the probability that a. All are defective. b. None are defective.
The probability that all selected transistors are defective is approximately 0.0014, while the probability that none of the selected transistors are defective is 0.1762.
Given:
Transistors = 13
Defective = 4
a. The number of ways to choose 4 defective transistors from the 4 available = [tex]^4C_4[/tex]
= [tex]\dfrac{4!}{4! 0!}[/tex]
= 1
and, the total number of ways to choose 4 transistors from the 13 available
[tex]^{13}C_4= \dfrac{13!}{4! * (13-4)!}[/tex]
= [tex]\dfrac{(13 * 12 * 11 * 10)}{(4 * 3 * 2 * 1)}[/tex]
= 715
Therefore, the probability of selecting all defective transistors is:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1 / 715
= 0.0014
b. The number of ways to choose 4 non-defective transistors from the 9 available is
[tex]^{9}C_4= \dfrac{9!}{4! * (9-4)!}[/tex]
= [tex]\dfrac{(9 * 8* 7* 6)}{(4 * 3 * 2 * 1)}[/tex]
= 126
So, the probability of selecting none defective transistors is:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 126 / 715
= 0.1762
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Final answer:
The probabilities are calculated using combinations: the probability all selected transistors are defective is 1/C(13,4) or 0.13%, and the probability none are defective is C(9,4)/C(13,4) = 17.6%.
Explanation:
The student's question about probabilities can be answered using combinations and the basic principles of probability. We need to calculate the probability that out of 13 transistors, all 4 selected are defective, and then the probability that none are defective.
Probability All Are Defective
To find the probability that all 4 transistors selected are defective, we calculate the number of ways to pick 4 defective ones out of 4 (which is 1 way, since we only have 4 defective ones), and divide it by the number of ways to pick any 4 out of 13. Using combinations, we calculate:
Probability(all defective) = C(4,4) / C(13,4) = 0.13%.
Probability None Are Defective
To find the probability that none of the 4 selected transistors are defective, we calculate the number of ways to pick 4 non-defective ones out of 9 (since 13 total minus 4 defective leaves 9 non-defective), and divide it by the number of ways to pick any 4 out of 13:
Probability(none defective) = C(9,4) / C(13,4) = 17.6%
There are two newborns, Gary and Eric. The future lifetime of Gary is uniformly distributed between 0 to 60 years. The future lifetime of Eric is uniformly distributed between 0 to 40 years. Their future lifetimes are independent. Calculate the probability that Gary dies first.
Answer: 0.25
Step-by-step explanation:
Given : The future lifetime of Gary is uniformly distributed with interval [0 years , 60 years].
Then the probability density function for Gary's future lifetime will be:-
[tex]f(x)=\dfrac{1}{60-0}=\dfrac{1}{60}[/tex]
The future lifetime of Eric is uniformly distributed with interval [0 years , 40 years].
Then the probability density function for Erin's future lifetime will be:-
[tex]f(x)=\dfrac{1}{40-0}=\dfrac{1}{40}[/tex]
Now, the joint density function for Gary and Eric's future lifetime :-
[tex]f(x,y)=f(x)f(y)=\dfrac{1}{40\times60}=\dfrac{1}{2400}[/tex] [∵Their future lifetimes are independent. ]
Now, the probability that Gary dies first is given by :-
[tex]\int^{60}_{0}\int^{40}_{x}f(x,y)\ dy\ dx\\\\=\int^{60}_{0}\int^{40}_{x}\dfrac{1}{2400}\ dy\ dx\\\\=\int^{60}_{0}\dfrac{40-x}{2400}\ dx\\\\=\dfrac{1}{2400}[40x-\dfrac{x^2}{2}]^{60}_{0}\\\\=\dfrac{1}{2400}(2400-\dfrac{3600}{2})=0.25[/tex]
Hence, the probability that Gary dies first =0.25
Cosella is conducting an experiment where she assesses how quickly teenagers can run a 100-meter race after consuming specific amounts of caffeine. She divides her sample up into three groups. Group 1 receives a glass of water with no caffeine added. Group 2 receives a glass of water with an amount of caffeine equivalent to that in one cup of coffee. Group 3 receives a glass of water with an amount of caffeine equivalent to that in two cups of coffee. Each participant is then timed as they run the course. In this study, the independent variable is
a. the previous running experience of each participant
b. the teenagers who are being studied
c. the time it takes to run the 100-meter race
d. the amount of caffeine being ingested
Answer:
c. the time it takes to run the 100-meter race
Step-by-step explanation:
An independent variable is the variable which is not being controlled and it does not depend on the other variables. This is the variable which is being studied/measured in the experiment.
Option a. The previous running experience is not being considered and is not a variable under study in this case. So this is not the answer.
Option b. The teenagers who are being studied constitute the sample. These are not the variables.
Option c. Time is the independent variable, as it is being measured during the experiment and the conclusion is being drawn based on it.
Option d. Amount of caffeine is being decided by Cosella and is therefore not the independent variable.
Therefore, the correct answer is option c
A bag contains 9 marbles: 3 are green, 4 are red, and 2 are blue. Lashonda chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue? Write your answer as a fraction in simplest form.
Answer:
2/9
Step-by-step explanation:
Because there's 2 blue marbles and 9 in total
Which number is graphed on the following number line?
Answer:
Step-by-step explanation:
looks like it's about 1/2
Looks approximately like x = 0.6 ish
are there MCQ choices?
In triangle ABC AD/DB = CE/EB. Complete the proof showing the segment DE is parallel to segment AC.
1.
a) (AD/DB) + 1 = (CE/EB) + 1
b) (AD/DB) + DE = (CE/EB) + DE
c) AD * EB = CE * DB
2.
a) Corresponding sides of congruent triangles are congruent.
b) Addition Property of Equality
c) cross multiplication
Edit: Answer is 1.A and 2.B (verified correct) thanks to
https://brainly.com/question/1428177
Answer:
1. [tex]\dfrac{AD}{DB}+1=\dfrac{CE}{EB}+1[/tex]
2. Addition property of equality
Step-by-step explanation:
In triangle ABC,
[tex]\dfrac{AD}{DB}=\dfrac{CE}{EB}.[/tex]
The addition property of equality states that if the same amount is added to both sides of an equation, then the equality is still true.
Use addition property of equality, add 1 to both sides of previouse equality:
[tex]\dfrac{AD}{DB}=\dfrac{CE}{EB}\\ \\\dfrac{AD}{DB}+1=\dfrac{CE}{EB}+1\\ \\\dfrac{AD+DB}{DB}=\dfrac{CE+EB}{EB}[/tex]
Answer:
(AD/DB) +1 = (CE/EB) +1 -----> Addition Property of Equality
Find the distance between the points (0, –1) and (3, –3).
A. 25
B. 5
C. √13
D. 13
Answer:
C. √13
Step-by-step explanation:
The distance between two points is given by
d =sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt( (3-0)^2 + (-3--1)^2)
= sqrt( 3^2 + (-3+1)^2)
= sqrt( 9+(-2)^2)
= sqrt( 9+4)
= sqrt(13)
To answer this, you basically use Pythagoras' Theroem, but instead of:
[tex]c = \sqrt{a^{2} + b^{2}}[/tex]
it will be :
[tex]distance = \sqrt{(y - y1)^{2} + (x - x1)^{2} }[/tex]
So you are finding the squareroot of the (difference in y coordinates)² plus (difference in x coordinates) ²:
x is the x-coordinate of (0, -1) (so x = 0)
y is the y-coordinte of (0, -1) ( so y = -1)
x1 is the x coordinate of (3, -3) ( so x1 = 3)
y1 is the y coordinate of (3, -3) (so y1 = -3)
--------------------------------------------------
Now, lets find the distance between the two points, by substituting all of this values into the equation at the top:
[tex]distance = \sqrt{(y - y1)^{2} + (x - x1)^{2} }[/tex] (substitute in values)
[tex]distance = \sqrt{( 0 -3)^{2} + (-1 - -3)^{2} }[/tex] (simplify: note -1 - - 3 = -1 + 3)
[tex]distance = \sqrt{( -3)^{2} + (-1 +3)^{2} }[/tex] (simplify)
[tex]distance = \sqrt{( -3)^{2} + (2)^{2} }[/tex] (now square the numbers)
[tex]distance = \sqrt{9 + 4 }[/tex] (simplify)
[tex]distance = \sqrt{13 }[/tex]
___________________________________________
Answer:C. [tex]\sqrt{13}[/tex]
A rectangle's width is one-fourth of its length. Its area is 9 square units. The equation l(l) = 9 can be used to find l, the length of the rectangle. What is the length of the rectangle? 0.75 units 1.5 units 3 units 6 units
Answer:
6 units
Step-by-step explanation:
A rectangle's width is one-fourth of its length.
w = 1/4 l
area is 9 square units
A = l*w = 9
Replacing w with 1/4l
l * (1/4l) = 9
1/4 l^2 = 9
Multiply each side by 4 to clear the fraction
4 * 1/4 l^2 = 4*9
l^2 = 36
Take the square root of each side
sqrt (l^2) = sqrt(36)
l =6
Answer:
6 units
Step-by-step explanation:
Let the length = L
Then the width = L/4
area = length * width
area = L * L/4 = 9
L^2/4 = 9
L^2 = 36
L = 6 or L = -6
Since we are dealing with a length, we eliminate the negative answer.
Answer: 6 units
P.S. Your equation is incorrect. L(L) = 9 would work for a square with 4 congruent sides and area 9. Here the sides have different lengths. The equation is L(L/4) = 9.
Santi buys 2 t-shirts for $9.50 each, a 3-pack of socks for $7.95, and a pair of shoes for $49.95. The sales tax is 6. To the nearest cent, what is the total cost of Santi's purchases?
Answer:
$98.47
Step-by-step explanation:
1. 2(9.5) + 3 (7.95) + 49.95 = $92.80
6% • $92.80 = $5.57
$92.80 + $5.57 = $98.47
A Chi square test has been conducted to assess the relationship between marital status and church attendance. The obtained Chi square is 23.45 and the critical Chi square is 9.488. What may be concluded?
a. reject the null hypothesis, church attendance and marital status are dependent
b. reject the null hypothesis, church attendance and marital status are independent
c. fail to reject the null hypothesis, church attendance and marital status are dependent
d. fail to reject the null hypothesis, church attendance and marital status are independent
Answer: a. reject the null hypothesis, church attendance and marital status are dependent
Step-by-step explanation:
If the obtained chi-square value is greater than the critical chi square value then we reject the null hypothesis.Given : A Chi square test has been conducted to assess the relationship between marital status and church attendance. The obtained Chi square is 23.45 and the critical Chi square is 9.488.
Null hypothesis : There is no relationship between the variables.
Alternative hypothesis : There is a relationship between the variables.
Here we can see that the obtained chi-square (23.45) value is greater than the critical chi square value (9.488) , then we have to reject the null hypothesis.
So the correct answer is reject the null hypothesis, church attendance and marital status are dependent.
Given the obtained Chi-square 23.45 is greater than the critical Chi square 9.488, we reject the null hypothesis, implying there is a significant relation or dependence between marital status and church attendance.
Explanation:In a Chi square test, if the obtained Chi square value is higher than the critical Chi square value, it means that the observed data significantly deviates from what is expected under the null hypothesis. Therefore, in this case, where the obtained Chi square is 23.45 and the critical number is 9.488, we would reject the null hypothesis. Considering that the null hypothesis is generally posed under the assumption of no relation or independence between the variables being tested, rejecting it thus implies that there is a significant relationship or dependence between marital status and church attendance. Therefore, the correct answer to the question is a. reject the null hypothesis, church attendance and marital status are dependent
.
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These are the means and standard deviations for examples of heights from two kinds of trees.
Table:
Tree A - (Mean: 25ft) (Standard deviation: 5ft)
Tree B - (Mean: 60 ft) (Standard deviation: 12 ft)
Select the TWO true statement.
A. Tree A's heights are more spread out than tree B's heights.
B. Tree A's heights are less spread out than tree B's heights.
C. Tree A has a greater average height than tree B.
D. Tree A has a lower average height than tree B.
Step-by-step explanation:
Tree A's heights are less spread out than tree B's heights. Tree A has a lower average height than tree Bs
If 10 were added to each of the values in a data set that originally had a standard deviation of 6, the standard deviation of the resulting data would be 6 true false
Answer:
TRUE
Step-by-step explanation:
Changing the mean by adding the same number to every data value does not change the differences those values have from the new mean. Hence the standard deviation remains unchanged. If it was 6, it will be 6.
Answer:
True because standard divination stays the same
Step-by-step explanation:
What is the value of m < 3
Answer:
142°
Step-by-step explanation:
∠3 is an alternate exterior angle with ∠7, so is congruent to ∠7. ∠7 is supplementary to 38°, so has measure 180° -38° = 142°.
The measure of ∠3 is 142°.
Please help me. these problems
Answer:
1st problem:
Converges to 6
2nd problem:
Converges to 504
Step-by-step explanation:
You are comparing to [tex]\sum_{k=1}^{\infty} a_1(r)^{k-1}[/tex]
You want the ratio r to be between -1 and 1.
Both of these problem are so that means they both have a sum and the series converges to that sum.
The formula for computing a geometric series in our form is [tex]\frac{a_1}{1-r}[/tex] where [tex]a_1[/tex] is the first term.
The first term of your first series is 3 so your answer will be given by:
[tex]\frac{a_1}{1-r}=\frac{3}{1-\frac{1}{2}}=\frac{3}{\frac{1}{2}=6[/tex]
The second series has r=1/6 and a_1=420 giving me:
[tex]\frac{420}{1-\frac{1}{6}}=\frac{420}{\frac{5}{6}}=420(\frac{6}{5})=504[/tex].
What is the slope of the line with equation y-3=-1/2(x-2)
Answer:
[tex]m =-\frac{1}{2}[/tex]
Step-by-step explanation:
The equation of a line in the pending intersection form is:
[tex]y = mx + b[/tex]
Where m is the slope of the line and b is the intersection with the y axis.
In this case we have the following equation
[tex]y-3=-\frac{1}{2}(x-2)[/tex]
To find the slope of this line you must rewrite it in the form
[tex]y = mx + b[/tex]
Then we solve the equation for y.
[tex]y-3=-\frac{1}{2}(x-2)[/tex]
[tex]y=-\frac{1}{2}(x-2)+3[/tex]
[tex]y=-\frac{1}{2}x-2*(-\frac{1}{2})+3[/tex]
[tex]y=-\frac{1}{2}x+1+3[/tex]
[tex]y=-\frac{1}{2}x+4[/tex]
Note that [tex]m =-\frac{1}{2}[/tex]
Finally the slope is: [tex]m =-\frac{1}{2}[/tex]
The slope of the line with equation; y-3 = -1/2(x-2) is; slope, m = -1/2.
According to the question, the equation of the line in discuss is; y-3 = -1/2(x-2).
To determine the slope of the line, we need to rearrange the equation such that it resembles the slope-intercept form of the equation of a straight line as follows;
The equation of a straight line; y = mx + c.
Now, we expand the equation of the line and rearrange as follows;
y-3 = (-1/2)x -1y = (-1/2)x -1 + 3y = (-1/2)x + 2.By comparison, the slope of the line given bey the equation, y-3=-1/2(x-2) is; slope, m = -1/2.
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What are the slope and y-intercept of the linear function graphed to the left?
Answer:
y intercept equals 1
Step-by-step explanation:
y= -1/2x+1
the slope is -1/2
the y intercept is 1
An engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 130lb and 171lb. The new population of pilots has normally distributed weights with a mean of 137lb and a standard deviation of 28.9lb. If a pilot is randomly selected find the probability that his weight is between 130lb and 171lb
Answer: 0.4758
Step-by-step explanation:
Given : Mean : [tex]\mu=137\text{ lb}[/tex]
Standard deviation : [tex]\sigma =28.9\text{ lb}[/tex]
Also, the new population of pilots has normally distributed .
The formula to calculate the z-score :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x=130 lb .
[tex]z=\dfrac{130-137}{28.9}=-0.2422145\approx-0.24[/tex]
For x=171lb.
[tex]z=\dfrac{171-137}{28.9}=1.1764705\approx1.18[/tex]
The p-value =[tex]P(-0.24<z<1.18)=P(z<1.18)-P(z<-0.24)[/tex]
[tex]=0.8809999-0.4051651=0.4758348\approx0.4758348\approx0.4758[/tex]
Hence, the required probability : 0.4758
Tyler and Katie started a lemonade stand to raise money. They donated \dfrac{2}{10} 10 2 ? start fraction, 2, divided by, 10, end fraction of their profits to their school library, \dfrac{1}{10} 10 1 ? start fraction, 1, divided by, 10, end fraction to the animal shelter, and \dfrac{4}{10} 10 4 ? start fraction, 4, divided by, 10, end fraction to the food bank. They saved the rest to buy materials for their next project. What fraction of their profits did Tyler and Katie donate?
Answer:
[tex]\frac{7}{10}[/tex]
Step-by-step explanation:
Fraction of the amount donated to school library = [tex]\frac{2}{10}[/tex]
Fraction of the amount donated to animal shelter = [tex]\frac{1}{10}[/tex]
Fraction of the amount donated to food bank = [tex]\frac{4}{10}[/tex]
The rest of the amount was saved for next project.
Thus, the total fraction of the amount donated will be the sum of fractions of amount donated to school library, animal shelter and food bank.
i.e.
Fraction of the amount donated = [tex]\frac{2}{10}+\frac{1}{10}+\frac{4}{10} = \frac{7}{10}[/tex]
This means, Tyler and Katie donated [tex]\frac{7}{10}[/tex] of their profits.
Answer:−1.825
Step-by-step explanation:
What is the complementary event to drawing a blue marble? (check all that apply)
drawing a red marble
drawing a green marble
drawing a red or green marble
not drawing a blue marble
PLZ hurry I give brainly
The complementary event to drawing a blue marble includes any outcome other than drawing a blue marble. Therefore, drawing a red marble, a green marble, a red or green marble, or not drawing a blue marble, all are complementary events.
Explanation:In probability, the complementary event of an event represents all outcomes not covered by the original event. In this case, the original event is 'drawing a blue marble'. Thus, the complementary event would include any outcome other than drawing a blue marble.
Based on the options given:
Drawing a red marbleDrawing a green marbleDrawing a red or green marbleNot drawing a blue marbleAll these are complementary events to drawing a blue marble, as they all represent outcomes other than 'drawing a blue marble'.
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