Answers
Answer:
at least one solution
Step-by-step explanation:
Consistent solutions have at least one solution, but may have more than one solution. Intersecting lines and Lines that are the same are consistent solutions
Answer:
[tex]\boxed{Atleast\ one \ Solution}[/tex]
Step-by-step explanation:
A consistent system of equations have at least one solution. It can be more than that. There are no compulsions.
Related Questions
Which expression is equivalent to 2(5)^4
Answers
Answer:
2·5·5·5·5
Step-by-step explanation:
2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.
Reducing scrap of 4-foot planks of hardwood is an important factor in reducing cost at a wood-floor manufacturing company. Accordingly, engineers at Lumberworks are investigating a potential new cutting method involving lateral sawing that may reduce the scrap rate. To examine its viability, two independent, random, representative samples of planks were examined. One sample contained 200 planks which were sawed using the old method. The other sample contained 400 planks which were sawed using the new method. Sixty-two of the 200 planks were scrapped under the old method of sawing, whereas 36 of the 400 planks were scrapped under the new method.
Required:
a. Construct the 90% confidence interval for the difference between the population scrap rates between the old and new methods, respectively.
b. Write the null and alternative hypotheses to test for differences in the population scrap rates between the old and new cutting methods, respectively.
c. Using the part a results, can we conclude at the 10% significance level that the scrap rate of the new method is different than the old method?
Answers
Answer:
The critical value for two tailed test at alpha=0.1 is ± 1.645
The calculated z= 9.406
Step-by-step explanation:
Formulate the hypotheses as
H0: p1= p2 there is no difference between the population scrap rates between the old and new cutting methods
Ha : p1≠ p2
Choose the significance level ∝= 0.1
The critical value for two tailed test at alpha=0.1 is ± 1.645
The test statistic is
Z = [tex]\frac{p_1- p_2}\sqrt pq(\frac{1}{n_1} + \frac{1}{n_2})[/tex]
p1= scrap rate of old method = 62/200=0.31
p2= scrap rate of new method = 36/400= 0.09
p = an estimate of the common scrap rate on the assumption that the two rates are same.
p = n1p1+ n2p2/ n1 + n2
p =200 (0.31) + 400 (0.09) / 600
p= 62+ 36/600= 98/600 =0.1633
now q = 1-p= 1- 0.1633= 0.8367
Thus
z= 0.31- 0.09/ √0.1633*0.8367( 1/200 + 1/400)
z= 0.301/√ 0.13663( 3/400)
z= 0.301/0.0320
z= 9.406
The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that the 10% significance level that the scrap rate of the new method is different from the old method.
2000 people attended a baseball game. 1300 of the people attending supported the home team, while 700 supported the visiting team. What percentage of people attending supported the home team?
Answers
Answer:
Percentage of home team supporters =65%
Percentage of visiting team supporters =35%
Step-by-step explanation:
Total attendees=2,000 people
Home team supporters=1,300
Visiting team supporters=700
What percentage of people attending supported the home team?
Percentage of people attending who supported the home team = home team supporters / total attendees × 100
=1,300/2,000 × 100
=0.65 × 100
=65%
Visiting team supporters = visiting team supporters / total attendees
× 100
=700/2000 × 100
=0.35 × 100
=35%
Alternatively,
Visiting team supporters = percentage of total attendees - percentage of home team supporters
=100% - 65%
=35%
if the nth term is , then the (n+1)st is: Sorry if formatting is off, check the image to see the equation better!
Answers
Answer:
5
----------
( n+1)(n+2)
Step-by-step explanation:
5
----------
n ( n+1)
Replace n with n+1
5
----------
(n+1) ( n+1+1)
5
----------
( n+1)(n+2)
We replace every 'n' with n+1 and simplify
[tex]\frac{5}{(n+1)(n+1+1)} = \frac{5}{(n+1)(n+2)}[/tex]
The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). If q(t) = 4t³ – 1, what is p(t)?
Answers
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]q(t) = 4t^3-1\\\\(qop)(t)=q(p(t))=4\left( p(t) \right) ^3-1=4t-21\\\\p(t)^3=\dfrac{4t-21+1}{4}=\dfrac{4(t-5)}{4}=t-5\\\\p(t)=\sqrt[3]{t-5}[/tex]
Cheers.
Taking into account the definition of composite function, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].
What is composite functionThe composite function is one that is obtained through an operation called composition of functions, which consists of evaluating the same value of the independent variable (x) in two or more functions successively.
In other words, a composite function is generally a function that is written inside another function. The composition of a function is done by substituting a function into another function.
Solving a composite function means finding the composition of two functions.
Function p(t)The expression of the composite function (q∘p)(t) is read "p composite with q". This means that you should do the following compound function: q[p(t)].
The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). And q(t)=4t³ – 1. Then:
s(t)= q[p(t)]
4t -21= 4[p(t)]³ – 1
Solving:
4t -21 +1= 4[p(t)]³
4t -20 = 4[p(t)]³
(4t -20)÷ 4 = [p(t)]³
4t÷4 -20÷ 4 = [p(t)]³
t -5 = [p(t)]³
[tex]\sqrt[3]{t-5}=p(t)[/tex]
Finally, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].
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Factor this trinomial completely. -6x^2 +26x+20
Answers
Answer:
Step-by-step explanation:
-6x²+26x+20
=-2(3x²-13x-10)
=-2(3x²-15x+2x-10)
=-2[3x(x-5)+2(x-5)]
=-2(x-5)(3x+2)
Suppose x varies directly with the square root of y and inversely with the cube root of z. What equation models this combined variation?
Answers
Answer:
[tex]\huge\boxed{x = k \frac{\sqrt{y} }{\sqrt[3]{z} }}[/tex]
Step-by-step explanation:
Given that:
1) x ∝ √y
2) x ∝ [tex]\frac{1}{\sqrt[3]{z} }[/tex]
Combining the proportionality
=> x ∝ [tex]\frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]
=> [tex]x = k \frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]
Where k is the constant of proportionality.
Why is f (x) = (3x + 1/3)^2 + 8/9 not the vertex form of f (x)
not the vertex form of f (x) = 9x^2 +2x +1?
O The expression has a constant outside of the squared term.
O Some of the terms are fractions instead of integers.
O The expression is not the product of two binomials.
O The variable x has a coefficient.
Answers
Answer:
The Variable has a coefficient.
Step-by-step explanation:
A report states that the mean yearly salary offer for students graduating with a degree in accounting is $48,722. Suppose that a random sample of 50 accounting graduates at a large university who received job offers resulted in a mean offer of $49,870 and a standard deviation of $3900. Do the sample data provide strong support for the claim that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722? Test the relevant hypotheses using α = 0.05. State your conclusion.A. Reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.B. Do not reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.C. Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.D. Do not reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Answers
Answer:
Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Step-by-step explanation:
First of all let's define the hypothesis;
Null hypothesis;H0; μ = $48,722
Alternative hypothesis;Ha; μ > $48,722
Now, let's find the test statistic for the z-score. Formula is;
z = (x' - μ)/(σ/√n)
We are given;
x' = 48,722
μ = 49,870
σ = 3900
n = 50
Thus;
z = (49870- 48722)/(3900/√50)
z = 2.08
So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526
This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722
A portion of the quadratic formula proof is shown. Fill in the missing reason.
Answers
Answer:
Find a common denominator on the right side of the equation
Step-by-step explanation:
The equation before the problem is
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
The next step in solving the above equation is to fibd tge common denominator on the right side of the equation.
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
X² + b/a(x) + (b/2a)²= -4ac/4a² + b²/4a²
X² + b/a(x) + (b/2a)²=( b²-4ac)/4a²
The right side of the equation now has a common denominator
The next step is to factorize the left side of the equation.
(X+b/2a)²= ( b²-4ac)/4a²
Squaring both sides
X+b/2a= √(b²-4ac)/√4a²
Final equation
X=( -b+√(b²-4ac))/2a
Or
X=( -b-√(b²-4ac))/2a
What is credit?
an arrangement in which you receive money, goods, or services now in exchange for the promise of payment later
an arrangement in which you receive goods or services in exchange for other goods and services
an arrangement in which you receive money now and pay it bulk later with fees?
Answers
Which table represents a linear function?
x y
1 5
2 10
3 15
4 20
5 25
x y
1 5
2 20
3 45
4 80
5 125
x y
1 5
2 25
3 125
4 625
5 3125
x y
1 2
2 4
3 7
4 16
5 32
Answers
Answer:
The first table on the list:
x 1 2 3 4 5
y 5 10 15 20 25
Step-by-step explanation:
A linear equation is when the slope is the exact same between each point. The way we find slope is by finding the change in "y" over the change in "x".
x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5
x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5
x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5
x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5
The slope for each change in points is 5, which means that this table represents a linear function.
The only table that represents a linear function is; Table 1
Linear functionA linear function is one that has the same slope for every coordinate point.
Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;
At x = 1, y = 5 and;Slope = 5/1 = 5
At x = 2; y = 10 and;Slope = 10/2 = 5
At x = 3, y = 15 and;Slope = 15/3 = 5
At x = 4, y = 20 and;Slope = 20/4 = 5
At x = 5, y = 25 and;slope = 25/5 = 5
In conclusion, only table 1 represents a linear function.
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CD is the perpendicular bisector of XY Determine the value of x. Question 8 options: A) –2 B) –1∕2 C) 4 D) 1.25
Answers
Answer:
Step-by-step explanation:
12x - 9 = 8x + 7
4x - 9 = 7
4x = 16
x = 4
solution is C
The solution is Option C.
The value of x is given from the equation x = 4
What is perpendicular bisector?A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.
The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn
Given data ,
Let the first line be represented as CD
Let the second line be represented as XY
Now , CD is the perpendicular bisector of XY
So , the point F is the midpoint of the line segment XY
The measure of line segment XF = 12x - 9
The measure of line segment FY = 8x + 7
From the perpendicular bisector theorem ,
The measure of line segment XF = The measure of line segment FY
Substituting the values in the equation , we get
12x - 9 = 8x + 7
Subtracting 8x on both sides of the equation , we get
4x - 9 = 7
Adding 9 on both sides of the equation , we get
4x = 16
Divide by 4 on both sides of the equation , we get
x = 4
Therefore , the value of x = 4
Hence , the value of the equation is x = 4
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(08.01 MC)
The volume of a pyramid that fits exactly inside a cube is 9 cubic feet. What is the volume of the cube? (5 points)
Select one:
a. 3 cubic feet
b. 6 cubic feet
c. 18 cubic feet
d. 27 cubic feet
Answers
Answer:
d. 27 cubic feet
Step-by-step explanation:
volume of cube = s^3 = B * s
volume of pyramid = (1/3) * B * h
The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.
volume of pyramid = 9 cu ft
volume of cube = 3 * 9 cu ft = 27 cu ft
Answer: d. 27 cubic feet
Answer:
27 ft^3 (Answer d)
Step-by-step explanation:
Here the volume of the pyramid is (1/3) the volume of the cube:
Letting s represent the length of one side of the base,
(1/3)(s)^2(s) = 9 ft^3, equivalent to s^3 = 27.
Solving for s, we get s = 3 ft.
Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)
True or False. The statistician should use Printout C to perform a t-test on the GROUP variable in the regression model. g
Answers
Answer:
False
Step-by-step explanation:
Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.
What is the area, in square meters, of the shaded part of the rectangle shown below?
Answers
Answer:
C) 100 cm²
Step-by-step explanation:
(14*6)/2*10
20/2*10
10*10
100
The area of the given shaded part of the rectangle is 100 square meters as shown.
What is the area of a triangle?The entire space filled by a triangle's three sides in a two-dimensional plane is defined as its area.
The fundamental formula for calculating the area of a triangle is A = 1/2 b h.
The area of the shaded part = area of the rectangle - area of the triangle
The area of the shaded part = 14 × 10 - (1/2) × 8 × 10
The area of the shaded part = 140 - 80/2
The area of the shaded part = 140 - 40
Apply the subtraction operation, and we get
The area of the shaded part = 100 meters²
Thus, the area of the given shaded part of the rectangle is 100 square meters.
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Solve for x (x+4)/3 = 2.
a. x = -2
b. x=2
c. x = 2/3
d. x= -10/3
Answers
Answer:
The answer is option BStep-by-step explanation:
[tex] \frac{x + 4}{3} = 2[/tex]
To solve it first of all cross multiply
That's
x + 4 = 6
Move 4 to the right side of the equation
The sign changes to negative
That's
x = 6 - 4
We have the final answer as
x = 2Hope this helps you
The manager of the video department at a department store plans to purchase a large number of DVDs of a recent movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling boxes of 14 DVD movies for $170. Only complete boxes of DVD movies can be purchased. Complete part a) and b) below. a)
a) If the manager can purchase boxes of DVD movies from either or both suppliers, determine the maximum number of DVD movies that can be purchased for $415. Indicate how many boxes of 20 and how many boxes of 14 will be purchased.
— box(es) of 20 and — box(es) of 14
b) How much will the DVD movies cost?
They will cost $—
Answers
Answer:
1 box of 20 and 1 box of 14
They will cost $410
Step-by-step explanation:
1. Find how many boxes of 20 DVD movies can be bought
415 - 240 = 175
1 box of 20 DVD movies can be sold
2. Find how many boxes of 14 DVD movies can be bought from $175
175 - 170 = 5
1 box of 14 DVD movies can be bought
3. Find the cost
240 + 170 = 410
Mark has a collection of 80 coins. There are only nickels and dimes in the collection. The total value of the coins is $5.00. How many dimes does Mark have?
Answers
Answer:
number of nickel = 60
number of dimes = 20
Step-by-step explanation:
1 nickel = 5 cents
1 dimes = 10 cents
$1 = 100 cents
we will use these value to solve the questions
_______________________________
Total no of coins = 80
let the number of nickels be x
let the number of dimes be y
thus,
x+y = 80
y = 80-x equation 2
value of x nickels = 5x
value of y dimes = 10y
Total value of x nickels and y dimes = 5x+10y
The total value of the coins is $5.00
total value of the coins in cents = 5*100 = 500
thus
5x+10y = 500
using y = 80-x from equation 2
5x + 10(80 - x) = 500
5x + 800 - 10x = 500
-5x = 500 - 800 = -300
x = -300/-5 = 60
Thus,
number of nickel = 60
number of dimes = 80-60 = 20
What is the issue with the work? It is wrong. Please answer this for points!
Answers
Answer:
3 ( a ) : x = 3.6,
3 ( b ) : x = 5
Step-by-step explanation:
For 3a, we can calculate the value of x through Pythagorean Theorem, which seemingly was your approach. However, the right triangle with x present as the leg, did not have respective lengths 9.6 and 12. The right angle divides 9.6 into two congruent parts, making one of the legs of this right triangle 9.6 / 2 = 4.8. The hypotenuse will be 12 / 2 as well - as this hypotenuse is the radius, half of the diameter. Note that 12 / 2 = 6.
( 4.8 )² + x² = ( 6 )²,
23.04 + x² = 36,
x² = 36 - 23.04 = 12.96,
x = √12.96, x = 3.6
Now as you can see for part b, x is present as the radius. Length 3 forms a right angle with length 8, dividing 8 into two congruent parts, each of length 4. We can form a right triangle with the legs being 4 and 3, the hypotenuse the radius. Remember that all radii are congruent, and therefore x will be the value of this hypotenuse / radius.
( 4 )² + ( 3 )² = ( x )²,
16 + 9 = x² = 25,
x = √25, x = 5
What number is the opposite of -3?
Explain your reasoning
Answers
Answer Explanation:
Lori buys a $586 certificate of deposit (CD) that earns 6.6% interest that compounds monthly. How much will the CD be worth in 13 years? Express your answer rounded correctly to the nearest cent. Do not include units on your answer.
Answers
Answer:
$1344.9Step-by-step explanation:
This problem can be solved using the compound interest formula
[tex]A= P(1+r)^t[/tex]
Given data
A, final amount =?
P, principal = $586
rate, r= 6.6% = 0.066
Time, t= 13 years
Substituting our values into the expression we have
[tex]A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87[/tex]
To the nearest cent the in 13 years the CD will be worth $1344.9
While walking from the car into your dormitory you dropped your engagement ring somewhere in the snow. The path is 30 feet long. You are distraught because the density of its location seems to be constant along this 30-foot route. a) What is the probability that the ring is within 12 feet of your car
Answers
Answer:
0.4
Step-by-step explanation:
we are required to find the probability that the ring is within 12 meters from nthe car.
we start by defining a random variable x to be the distance from the car. the car is the starting point.
x follows a normal distribution (0,30)
[tex]f(x)=\frac{1}{30}[/tex]
[tex]0<x<30[/tex]
probabilty of x ≤ 12
= [tex]\int\limits^a_ b{\frac{1}{30} } \, dx[/tex]
a = 12
b = 0
[tex]\frac{1}{30} *(12-0)[/tex]
[tex]\frac{12}{30} = 0.4[/tex]
therefore 0.4 is the probability that the ring is within 12 feet of your car.
Find y using the Angle Sum Theorem
Answers
Step-by-step explanation:
Hey, there!!
Look this figure, simply we find that;
In triangle ABC,
angle CBD is an exterior angle of a triangle.
and its measure is 90°
Then,
angle CBD= y +48° {sum of interior opposite angle is equal to exterior angle or from theorem}.
or, 90°= y + 48°
Shifting, 48° in left side,
90°-48°= y
Therefore, the value of y is 42°.
Hope it helps...
Which is an infinite arithmetic sequence? a{10, 30, 90, 270, …} b{100, 200, 300, 400} c{150, 300, 450, 600, …} d{1, 2, 4, 8}
Answers
Answer:
C
Step-by-step explanation:
An arithmetic sequence has a common difference d between consecutive terms.
Sequence a
30 - 10 = 20
90 - 30 = 60
270 - 90 = 180
This sequence is not arithmetic
Sequence b
200 - 100 = 100
300 - 200 = 100
400 - 300 = 100
This sequence is arithmetic but is finite, that is last term is 400
Sequence c
300 - 150 = 150
450 - 300 = 150
600 - 450 = 150
This sequence is arithmetic and infinite, indicated by ........ within set
Sequence d
2 - 1 = 1
4 - 2 = 2
8 - 4 = 4
This sequence is not arithmetic
Thus the infinite arithmetic sequence is sequence c
Can someone please help me?
Answers
Negative Integers are :
Less than zeroTo the left of zero on a number line.Help Me With This
show work
Answers
Answer:
1. Make a list of activities and the number of students:
Watching TV: 32
Talking on the phone: 41
Video games: 24
Reading: 15
2. Then combine the data in a bar graph as shown in the picture
if y = 2√x÷ 1–x', show that dy÷dx = x+1 ÷ √x(1–x)²
Answers
Answer: see proof below
Step-by-step explanation:
Use the Quotient rule for derivatives:
[tex]\text{If}\ y=\dfrac{a}{b}\quad \text{then}\ y'=\dfrac{a'b-ab'}{b^2}[/tex]
Given: [tex]y=\dfrac{2\sqrtx}{1-x}[/tex]
[tex]\sqrtx[/tex][tex]a=2\sqrt x\qquad \rightarrow \qquad a'=\dfrac{1}{\sqrt x}\\\\b=1-x\qquad \rightarrow \qquad b'=-1[/tex]
[tex]y'=\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)}{(1-x)^2}\\\\\\.\quad =\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)\bigg(\dfrac{\sqrt x}{\sqrt x}\bigg)}{(1-x)^2}\\\\\\.\quad =\dfrac{1-x+2x}{\sqrt x(1-x)^2}\\\\\\.\quad =\dfrac{x+1}{\sqrt x(1-x)^2}[/tex]
LHS = RHS: [tex]\dfrac{x+1}{\sqrt x(1-x)^2}=\dfrac{x+1}{\sqrt x(1-x)^2}\qquad \checkmark[/tex]
Ajar contains 4 red marbles numbered 1 to 4 and 10 blue marbles numbered 1 to 10. A marble is
drawn at random from the jar. Find the probability of the given event.
(a) The marble is red
Your answer is:
(b) The marble is odd-numbered
Your answer is:
(C) The marble is red or odd-numbered
Your answer is:
(d) The marble is blue or even-numbered
Your answer is:
Question Help M Message instructor
Answers
Answer:
a)2/7
b)1/2
c)9/14
d)6/7
Step-by-step explanation:
The jar contains 4 red marbles, numbered 1 to 4 which means
Red marbles = (R1) , (R2) , (R3) , (R4)
It also contains 10 blue marbles numbered 1 to 10 which means
Blue marbles = (B1) , (B2) , (B3) , (B4) , (B5) , (B6) , (B7) , (B8) , (B9) , (B10) .
We can calculate total marbles = 4red +10 blues
=14marbled
Therefore, total marbles= 14
The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10) =7
Total number of Blue marbles = 10
Blue and even marbles = 5
(a) The marble is red
P(The marble is red)=total number of red marbles/Total number of marbles
=4/14
=2/7
(b) The marble is odd-numbered
Blue marbles with odd number= (B1) , (B3) , (B5) , (B7) , (B9) ,
Red marbles with odd number = (R1) , (R3)
Number of odd numbered =(5+2)=7
P(marble is odd-numbered )= Number of odd numbered/ Total number of marbles
P(marble is odd-numbered )=7/14
=1/2
(C) The marble is red or odd-numbered?
Total number of red marbles = 14
Number of red and odd marbles = 2
The marbles that has odd number = (R1) , (R3) ,(B1) , (B3) , (B5) , (B7) , (B9) =7
n(red or even )= n(red) + n(odd)- n(red and odd)
=4+7-2
=9
P(red or odd numbered)= (number of red or odd)/(total number of the marble)
= 9/14
(d) The marble is blue or even-numbered?
Number of Blue and even marbles = 5
Total number of Blue marbles = 10
Number of blue that are even= 5
The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10)
=7
n(Blue or even )= n(Blue) + n(even)- n(Blue and even)
= 10+7-5 =12
Now , the probability the marble is blue or even numbered can be calculated as
P(blue or even numbered)= (number of Blue or even)/(total number of the marble)
= 12/14
= 6/7
Officer Jacobi drove 180 miles in his patrol car during part of May. The distance represents 40% of May. How many miles did he drive all of May? a) 710 miles b) 420 miles c) 720 miles d) 450 miles Need Help on How to work this problem out, what formula would I use?
Answers
Answer:
D: 450 miles
Step-by-step explanation:
So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):
[tex]0.4D=180[/tex]
This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:
[tex]0.4D=180\\D=450[/tex]
So the answer is D or 450 miles.
Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.
Explanation: When doing percentages, we can use the proportion is/over=%/100.
If we apply this to your problem, we can say 180 miles “is” 40% “of” x (x is the total number of miles driven in May.
Plugging in numbers for is, of, and the % gives us 180/x=40/100
Solving with cross multiplying and dividing gives us 450 miles=x
