Answer: y = -3x + 6
Step-by-step explanation:
If it is perpendicular to the line -3x + 2, then it's slope should also be -3.
The standard form of a line is y = mx + b. As our slope is -3, we have that our line is y = -3x+b. Now, let's put the given point into the line. x = 3 and y = -3, so -3 = -3*3 + b. Hence, b = -3+9 = 6. The equation of the line is y = -3x + 6.
1. Maria's new car costs $280 per month for
car payments and insurance. She estimates
that gas and maintenance cost 15 cents per
mile.
a) Express her total monthly cost as a
function of the miles driven during the
month.
b) What is the slope of the graph of the cost
function?
From the situation described, it is found that:
a) The linear function that expresses her monthly cost is:
C(m) = 280 + 0.15m.
b) The slope of the graph of the cost function is of 0.15.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).In the context of the cost function in this problem:
The intercept is the fixed cost per month, for cay payments and insurance, of $280.The slope is the variable cost, which is the cost per mile of 15 cents = $0.15.Hence the parameters of the function are given as follows:
m = 0.15, b = 280.
The cost function for a mileage of m miles is, considering the above coefficients, is given by:
C(m) = 0.15m + 280.
With the slope of 0.15 already explained.
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carson flips over the cards of a standard 52-card deck one at a time. what is the probability that he flips over the ace of spades before any face card (jack, queen or king)?
The probability that the ace of spades will be revealed before any face card (the jack, queen, or king) is 0.0769.
What in mathematics is probability?Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.
The likelihood is based on the range of potential outcomes. the total number of possible outcomes. As an illustration, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head.
According to given data;
Let's look at the first few probabilities; we're going to do this in reverse order, in order to find a pattern:
P(O,O,O,AS)=39/52)*(38/51)*(37/50)*(1/49)
=(39*38*37/3!)/(52*51*50/3!)*1/49
P(O,O,AS)=(39/3)(52/3)×1/49
but we know that;
(n/2)=n(n-1)/2!
P,(O,O,AS) =(39/2)/(52/2) *1/50
P(AS)=(39/0)/(52/0) *(1/52)
We now have
P(AS)+P(O,AS)+P(O,O,AS)+P(O,O,O,AS)
FROM THIS CALCULATE ;
P=0.0769
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a large national study finds that 10% of pregnant women deliver prematurely. a local obstetrician is seeing 20 pregnant women in the next week at their clinic. (round answers to 3 decimal places)
The probability that fewer than 3 women will deliver prematurely is 1/20.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The total number of positive outcomes as well as the probability of any given event depend on each other. The probability is typically defined as the proportion of favorable outcomes to all outcomes in the sample space. Probability of an event P(E) = (Number of favorable outcomes) ÷ (Sample space).So, 10% of 20:
20/100 × 10 = 2 (Which is less than 3)Then, Premature delivery (Of fewer than 3 women) = 1Total events = 20P(E) = favourable/total events1/20Therefore, the probability that fewer than 3 women will deliver prematurely is 1/20.
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The correct question is given below:
A large national study finds that 10% of pregnant women deliver prematurely. a local obstetrician is seeing 20 pregnant women in the next week at their clinic. what is the probability that fewer than 3 of them will deliver prematurely?
Find the equation of a line perpendicular to y=3x+3 that passes through the point (3,2)
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{3} x + 3\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{3\implies\cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}[/tex]
so we're really looking for the equation of a line whose slope is -1/3 and that is passes through (3 , 2)
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y-2=- \cfrac{1}{3}x+1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{3}x+3 \end{array}}[/tex]
What are the domain and range of this relation? pt2
Answer:
Domain: { -5, -1, 1, 3, 4}
Range: { -2, 1, 5}
Step-by-step explanation:
Domain = X-Values
Range = Y-Values
Every possible X-Value is the domain, and likewise with the Range.
Meaning if it was a line that went on forever through Y-1 the the Domain would be X = {-[infinity], +[infinity]} and the range would be Y = {1}
Hope this helps.
12 eggs cost $2.56. How much is one egg? (unit rate)
Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
#y
○_f(x) = x(x − a)²(x −b)4
f(x) = x(x − a)³(x − b)²
f(x) = x²(x-a)(x - b)²
O f(x) = x²(x-a)5(x - b)
X
Answer: C
f(x)= x^4(x-a)(x-b)^2
Answer:
[tex]f(x)=x^4(x-a)(x-b)^2[/tex]
Step-by-step explanation:
The graph of a polynomial function will:
touch the x-axis at zeros with even multiplicities. cross the x-axis at zeros with odd multiplicities.The zero at the origin (0, 0) touches the x-axis and so it has an even multiplicity (exponent). Therefore, we can immediately discount the first two answer options as both have x as a zero (x = x¹ so its exponent is odd).
The end behavior of the graphed function means the leading coefficient is positive and the degree of the polynomial is odd.
The sum of the multiplicities is the degree of the polynomial function.
[tex]f(x)=x^4(x-a)(x-b)^2 \implies \textsf{Sum of multiplicities}: 4+1+2=7[/tex]
[tex]f(x)=x^2(x-a)^5(x-b) \implies \textsf{Sum of multiplicities}: 2+5+1=8[/tex]
Therefore, the only function that could represent the given graph is
[tex]\boxed{f(x)=x^4(x-a)(x-b)^2}[/tex]
as its degree is odd and it has a zero at the origin with even multiplicity.
Please help me I need help
Answer:
16 and -16
Step-by-step explanation:
Answer: D. 16 and -16
Step-by-step explanation: I dont think you need an explanation because it is multiple choice.
2 odd numbers that are a factor of 30 and multiples of 5
Answer:
Step-by-step explanation:
The required two odd numbers are 3 and 5.
We have to determine, It is a factor of 30 and a multiple of 3 what are 2 numbers.
To obtain the factor of 30 and 2 numbers is calculated in the following steps.
The Factors of 30 are,
30 = 2 , 3 , 5 ,
And multiply the terms by 2,
After multiply by 2 all the term become even.
Then,
The 2 odd numbers are: 3, 5
Hence, The required two odd numbers are 3 and 5.
The hypotenuse of a right triangle measures 20 cm and one of its legs measures 7 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
19
Step-by-step explanation:
The square value of the measure of hypotenuse is equal to the square measure of sum of two legs.
Let x represent the missing leg:
[tex] {20}^{2} = {7}^{2} + {x}^{2} [/tex]
400 = 49 + x^2 subtract 49 from both sides
351 = x^2 find the root for both sides
The root of 351 is between 18 and 19 but it is closer to 19 since 19×19 = 361 and since we are asked to round to the nearest tenth the answer is 19.
Identify the GCF of the following terms; 18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7
The greatest common factor of the given terms is 2a⁴b
Greatest Common Factor (GCF)From the question, we are to determine the greatest common factors of the given terms
The given terms are
18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7
That is,
18a⁴b⁹c² and 34a⁶b⁵ and 22a⁸bc⁷
We will express each of the given terms as a product of their factors
18a⁴b⁹c² = 2 × 3 × 3 × a⁴ × b⁸ × b × c²
34a⁶b⁵ = 2 × 17 × a⁴ × a² × b⁴ × b
22a⁸bc⁷ = 2 × 11 × a⁴ × a⁴ × b × c⁷
Hence, the GCF is 2 × a⁴ × b = 2a⁴b
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Milly measured a cereal box It is two inches wide six inches long and twelve inches tall what is the volume of the cereal box
The volume of the cereal box is 144 square inches its width is two inches, its length is six inches and its height is 12 inches.
What is the volume of a rectangular prism?The top, bottom, and lateral faces of a rectangular prism are all rectangles, and all the pairs of opposing faces are congruent. A rectangular prism is a three-dimensional structure with six faces.
The rectangular prism's base area is equal to lw (using the area of a rectangle formula)
The height of the rectangle prism is equal to h.
Thus, V = lw ×h = lwh is the formula for the rectangular prism's volume.
Given,
width = 2 inches
length = 6 inches
height = 12 inches
The volume of a rectangular prism is simply length× width× height.
Volume = 6× 2× 12
= 144 square inches.
Therefore, the volume of the cereal box is 144 square inches.
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Assume that TUVE AWXY. Which of the following congruence statements
are correct? Check all that apply.
A. TU = YX
B. ZULT
C.LY/V
D. ZW= LT
E. ZX=ZT
☐ F. VU = WX
Whoever can answer this gets branliest!!
A baseball player batted 544 times in a season, with a batting average of 0.294. Using the formula below, find the number of hits he made.
The batting average formula is a = h/n where a is the batting average ,h is the number of hits and n is the number of times at bat
A. 148 hits
B. 160 hits
C. 159 hits
D. 165 hits
Answer:
B. 160 hits
Step-by-step explanation:
544 × .294 = 159.936, which rounds to 160.
Write an equation of the line in point-slope form that passes through the given points.
(4,-5) and (-4,-8)
Answer: y+5=3/8*(x-4)
Step-by-step explanation: Find the slope using m = y2-y1/x2-x2 which is the change of y over change of x, so the slope is m=3/8. Use the slope 3/8, and a given point (4, -5) to substitute for x1 and y1 in point slope form y -y1 = m(x-x1). So y-(-5)=3/8*(x-(4)). Now we simplify the equation so it's y+5=3/8*(x-4).
Consider a goodness-of-fit test with a computed value of chi-square27. 385 and a critical value13. 388, the appropriate decision would be to __________.
Since the chi-square 27.385 is greater than 13.388 at the provided critical value level value, the null hypothesis is accepted.
What is conclusion of hypothesis testing?The hypothesis test makes an announcement the outcome of an assumption in five to six fundamental phases. The technique to be used is based on the idea of correlating the standardized sample equivalent of a parameter to the critical boundary that allows the null hypothesis to be accepted.For the given question;
27. 385 is the chi-square value.13.388 is the critical value.The hypotheses for the goodness of fit test are as follows:
Null: a expected value does not differ significantly from the observed values.Alternative: the expected value differs significantly from the observed values.The chi-square test has one tail.
The criterion is as follows:
The null hypothesis is dismissed if the test statistic exceeds the critical value.If the test statistic is less than the critical value, this same null hypothesis is rejected.Thus, the null hypothesis is accepted at the provided level of critical value because the chi-square 27.385 is more than 13.388.
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figure 1 and figure 2 below are similar. which point corresponds to point S.
Both figures 1 & 2 are similar
Point S in figure 1 corresponds to Point P in fugure 2
HELP IM CONFUSED. NEED HELP ASAP
Answer:
Yeah good job! u got it right :)
Step-by-step explanation:
How to find perimeter?
Frist you will add up all the sides
then thats your answer :)
In this case the same logic applies
Hope this helps :3
X
3
2
1
0
-1
-2
-2
Y
12
10
8
6
4
2
0
Find the domain and range
Answer:
domain: all x-values
Step-by-step explanation:
what is the equivalent fraction?
The equivalent fraction of 1 2/3 + 1 1/2 is 1 4/6 + 1 3/6
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators.
How to evaluate the fraction expression?The fraction expression is given as
1 2/3 + 1 1/2
Express the mixed numbers as improper fractions
So, we have
1 2/3 + 1 1/2 = 5/3 + 3/2
Rewrite as equivalent fractions
1 2/3 + 1 1/2 = 10/6 + 9/6
Express the improper fractions as mixed numbers
So, we have
1 2/3 + 1 1/2 = 1 4/6 + 1 3/6
Hence, the value of the expression is 1 4/6 + 1 3/6
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A number x divided by 36
Answer:
x/36 is what you're looking for my guy
Estimate the percentage of engineers that are chemical engineers using the following data
-Total number of engineers listed in this figure is approximately 1,326,800.
-chemical engineers: 27,860
Show work and type formulas Speed=distance=
Time
Based on the number of people who are engineers and those who are chemical engineers, the percentage who are chemical engineers is 2.01%
How to find the percentage?To find the percentage of something out of the total number, the formula is:
= Number of selected variables / Total number of variables x 100%
The selected variable here is chemical engineers so the percentage of chemical engineers out of the total number of engineers is:
= Number of chemical engineers / Total number of engineers x 100%
= 27,860 / 1,326,800 x 100%
= 2.01%
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I WILL GIVE 20 POINTS IF THE ANSWER IS CORRECT AND A GOOD EXPLANATION
The surface area of a cylinder is equal to 208π square units.How to calculate the surface area of right cylinder?The surface area is the sum of the areas of all faces of the solid. In the case of a right cylinder, the surface area is the sum of the two areas of the circular base and the lateral area (A), in square units, whose formula is described below:A = 2π · r² + 2π · r · h (1)Where:r - Base radiush - HeightIf we know that r = 8 and h = 5, then the surface area of the right cylinder is:A = 2π · 8² + 2π · 8 · 5A = 208πThe surface area of a cylinder is equal to 208π square units.
(3, -5)(7,-5)(7,2)(3,3)
Find the area of the rectangle
Answer: The answer could be 28 but I need to know what is the length and what is the height.
Step-by-step explanation:
I will just name the points for simplicity:
A - (3, -5)
B - (7, -5)
C - (7, 2)
D - (3, 3)
A to B - 4
B to C - 7
C to D - 4.1231
***
Distance (d) = √(3 - 7)^2 + (3 - 2)^2
= √(-4)^2 + (1)^2
= √17
= 4.1231056256177
***
D to A - 8
4 * 7 = 28
4 2/5 divide 1 1/5 need answer
Answer:
5 3/5
Step-by-step explanation:
assuming you are dividing fractions, here are your steps
867,000 rounded to the nearest ten thousand is
Answer:
870,000
Step-by-step explanation:
Ten thousand is 10,000.
The ten thousand value here is 6
The thousand value here is 7.
Using rounding rules, 5 and up goes up therefore the ten thousand value becomes 7.
867,000 --> 870,000
Hope that helps
how to solve please
The reasons that proves the congruency of the triangles are;
2.7 [tex] \Delta EDF \cong \Delta FGE[/tex] by SSS congruency postulate
2.8 [tex] \Delta AOB \cong \Delta COB[/tex], by SAS congruency rule
[tex] \Delta AOB \cong \Delta COB[/tex], by ASA congruency rule or postulate
What are the triangle congruency rules?The rules that proves two triangles to be congruent is if they satisfy any of the 5 rules of congruency, which are; Side–side–side, or SSS, side–angle–side, or SAS, side–angle–angle, or SAA, angle–side–angle, or ASA, and right angle–hypotenuse–side, or RHS
2.7 The given parameters of the two triangles are;
DE = GF, and DF = GE
Required;
To prove that
[tex] \Delta EDF \cong \Delta FGE[/tex]
Solution;
From the given diagram, we have;
[tex]EF \cong FE[/tex]
Reflexive property
Therefore;
[tex] \Delta EDF \cong \Delta FGE[/tex]
Side–Side–Side, SSS rule of congruency
The Side–Side–Side congruency postulate states that if the three sides of one triangle are congruent to three sides of another triangle, then both triangles are congruent.
2.8 The circle information are;
The midpoint (center) of the circle = Point O
Segment OB is perpendicular to segment AC, [tex] OB \perp AC [/tex]
OB bisects AC
Required;
To prove that [tex] \Delta AOB \cong \Delta COB[/tex]
Solution;
Segment OA and OC are the radius of circle O
Therefore;
[tex] OA \cong OC[/tex] by the properties of the radius of a circle
The angle [tex] \angle OAB \cong \angle OCB [/tex] ; Base angles of isosceles triangle ∆OAC
[tex] AB \cong BC[/tex], Segments formed by the perpendicular bisector OB
Given that AB, [tex] \angle OAB [/tex] and OA in [tex] \Delta AOB [/tex] are congruent to BC, [tex] \angle OCB [/tex] and OB in [tex] \Delta COB [/tex], we have;
[tex] \Delta AOB \cong \Delta COB[/tex] by Side–Angle–Side, SAS congruency postulateSecond proof;
Given that OB is the perpendicular bisector of AC, we have;
[tex] \angle OBA \cong \angle OBC = 90^{\circ} [/tex], definition of angles formed by perpendicular lines
[tex] AB \cong BC[/tex]
Therefore;
[tex] \Delta AOB \cong \Delta COB[/tex] by Angle–Side–Angle, ASA, congruency postulateLearn more about the triangle congruency here:
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A scale drawing of an elephant is shown. The actual
elephant that the model is based on is 216 inches long.
What is the scale factor for the model?
A. 1:30
B. 30:1
C. 208.8
D. 1555.2
The scale factor for the model of the elephant is 1 : 30 (option A).
What is the scale factor?A scale drawing is either a smaller or a larger version of an original image. For example, a map is a smaller version of a city, country or area.
A scale factor provides information on the relationship that exists between the scale drawing and the actual image. The scale factor shows the rate of reduction or enlargement of the original image.
Scale factor = actual length of the elephant / length of the elephant in the model
216 / 7.2 = 30
The scale factor is 1 : 30
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What is 20% of a 400 liter tank?
20% of a 400 liter tank is 80 liters.
what is the standard deviation of 0,0,1,1,1,2,2,3,5
Based on the numbers given in the distribution, the standard deviation can be found to be 1.49
How to find the standard deviation?To find the standard deviation, you first have to find the mean of the distribution:
= (0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 5 ) / 9
= 15 / 9
= 1.67
You can then find the variance using financial calculators to be:
= 2.2222222
The standard deviation is:
= √variance
= √2.2222222
= 1.49
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