Step-by-step explanation:
you made a typo.
since we are using only the digits 1, 3, 6 and 9, the list has to start
1, 3, 6, 9, 11, 13, 16, 19, 31, 33
it has to continue with
36, 39
we can skip the 40s and 50s and have then
61, 63, 66, 69
we can skip the 70s and 80s and have then
91, 93, 96, 99
that means we have 20 (5×4) numbers for the first 100.
we would have the corresponding 20 numbers in the 100s. like 101, 103, ...
but we have to skip 101, 103, 106, 109, because they contain 0.
so, it is only 16 numbers in the 100s.
there are none in the 200s.
then again 16 in the 300s. and the 600s and 900s.
so, we have
20 + 4×16 = 84 numbers in the first 1000.
then we have
16 in each the 1100s, the 1300s, the 1600s and 1900s.
and we have none in the 2000s.
so, in total we have
84 + 4×16 = 84 + 64 = 148 numbers to write.
Determine which of the lines, if any, are parallel or perpendicular. explain. line a passes through (2, 10) and (4, 13). line b passes through (4, 9) and (6, 12) . line c passes through (2, 10) and (4, 9) .
Line a and line b are parallel to each other, and c is neither parallel nor perpendicular.
Line a passes through (2, 10) and (4, 13).
Line b passes through (4, 9) and (6, 12).
Line c passes through (2, 10) and (4, 9).
If a line passes through two points, then the slope of the line is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Line a passes through (2, 10) and (4, 13). So, the slope of this line is
[tex]m_{a}=\frac{13-10}{4-2}=\frac{3}{2}[/tex]
Line b passes through (4, 9) and (6, 12). So, the slope of this line is
[tex]m_{b}=\frac{12-9}{6-4}=\frac{3}{2}[/tex]
Line c passes through (2, 10) and (4,9). So, the slope of this line is
[tex]m_{c}=\frac{9-10}{4-2}=\frac{1}{2}[/tex]
The product of slopes of perpendicular lines is -1.
and if the slope of 2 lines is equal then those lines are parallel
so, line a and line b are parallel to each other, and c is neither parallel nor perpendicular.
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F(x)=-2x-3 find f(-1)
Answer:
x = -1
Step-by-step explanation:
mark me on brainliest please follow me to
Answer:
-1
Step-by-step explanation:
Replace the variable x with 1 in the expression .
f(1)= 2(1) - 3
Remove the parenthasis
2(1) - 3
Multiply 2 by 1
2 - 3
subtract 2 from 3
-1
last year at a certain high school, 10 students sought the nomination for president of the student body. in how many ways could the voters (student body) rank their first 5 choices? a) 5 b) 50 c) 30,240 d) 3,628,800 e) 252 f) none of the above.
The number of ways voters could rank their first 5 choices out of 10 is 30240.
Given,
Number of students sought the nomination for president of the student body = 10 students
We have to find the number of ways voters could rank their first 5 choices.
Permutation;
An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.
Here we have to use permutation formula;-
ⁿPr = n! / (n - r)!
Here,
n is the number of students = 10
r is the choices = 5
Then,
ⁿPr = n! / (n - r)!
¹⁰P₅ = 10! / (10 - 5)!
¹⁰P₅ = 10! / 5!
¹⁰P₅ = 10 x 9 x 8 x 7 x 6
¹⁰P₅ = 30240
That is,
The number of ways voters could rank their first 5 choices out of 10 is 30240.
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A box of volume 216 m3 with a square bottom and no top is made of two different materials. the cost of the bottom is $40/m2 and the cost of the sides is $30/m2. find the dimensions of the box that minimize the total cost. (use symbolic notation and fractions where needed. write the objective function with respect to the length of the square bottom.)
The dimensions of the box that minimize total cost are height h =3.17m, width, w and length, l=9.52m are equal to .
How to find the height of the box ?Let h is the height of the box.
Given Volume of the box is 216 m³ with no top.
And the cost of the bottom is 40USD/m².
For the sides, it is 30USD/m².
The bottom of the box is square, so l = w.
So Volume
[tex]V=hl^{2}[/tex]
[tex]216=hl^{2}[/tex]
[tex]h=\frac{216}{l^{2} }[/tex]
Now Surface Area of the box without a top is
S = 4hl + l²
So,
cost = 4 × 30hl +40l²
cost = 120 hl + 40 l²
Putting h ,
cost = 120 × [tex](\frac{216}{l^{2} })l + 40l^{2}[/tex]
cost = [tex]\frac{25960}{l^{2} }+40l^{2}[/tex]
To find minimum cost, derivate the by using the calculator at
[tex]l=3\sqrt[3]{4}[/tex]
l=4.762203 m
[tex]h=\frac{216}{4.762203^{2} }[/tex]
h = 9.5244069354 m
Hence the dimensions of the box are
l=w
=9.52 m
and height ,h=3.17 m
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The value of function is positive so the function have maximum value 30 at x=3.
In the given question we have to find the maximum or the minimum value of a function.
The given function is
f(x) = -3x^2+18x+3
To find the maximum or minimum value we firstly find the value of f'(x).
f'(x) = -6x+18
Now put f'(x)=0
-6x+18=0
Subtract 18 on both side we get
-6x=-18
Divide by -6 on both side we get
x = 3
Now finding the value of function at x=3
f(3)= -3*(3)^2+18*3+3
f(3)= -3*9+54+3
f(3)= -27+54+3
f(3)= 30
Since the value of function is positive so the function have maximum value 30 at x=3.
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9. A family ordered 2 large pizzas for lunch. They ate
7
-
8
of one pizza and of the other pizza. What
fraction of a pizza was left for dinner?
118
b. 1/2
d. 12/12
b.
e.
318
334
C.
718
00
10
Answer:
9/16
Step-by-step explanation:
Jacob distributed a survey to his fellow students asking them how many hours they spent on the Internet in the past day. He also asked them to rate their mood on a scale from 0,10, with ten being the happiest. A line was fit to the data to model the relationship.
Answer:
The answer is B. y = -x + 7.5.
Step-by-step explanation:
The slope is -1 and the y-intercept is 7.5.
PLEASE MARK AS BRAINLIEST!!!Suppose m<4 =108 find m<5 and m<7
m ∠5 and m ∠7 is 72 ° . All straight angles are 180 degrees, according to the straight angle theorem. A straight angle is formed when the angle's legs point precisely in the opposite directions. The symbol for a straight angle is 180 degrees, or π (in radians).
How to find angle ?An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The names of basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle and full rotation. An angle is geometrical shape formed by joining two rays at their end-points. An angle is usually measured in degrees.
m ∠4 = 108°
m ∠5 = m ∠1
m ∠1 is in same line of m ∠4
So
m ∠1 = 180 - m ∠4
m ∠1 = 180 - 108
m ∠1 = 72 °
So m ∠5 = 72 °
m ∠7 is opposite to m ∠5 , opposite angles will be equal
Therefor m ∠7 = 72 °
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please help me with this math problem
Which expression is equivalent to -51 - (-60)−51−(−60)minus, 51, minus, left parenthesis, minus, 60, right parenthesis?
The required expression which is equivalent to -51 -(-60) is -51 + 60.
Given that,
Which expression is equivalent to -51 - (-60) is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression = -51 - (-60)
Simplify by applying the property of distribution under the parenthesis,
= -51 + 60
Thus, The required expression which is equivalent to -51 -(-60) is -51 + 60.
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A number is raised to the third power, then subtracted from 15 to get 7. What is the number squared?
Answer:
x=22
Step-by-step explanation:
Let the unknown number be x
:- the power of x = x³
From the question
x³-15=7 and x²
x³=7+15
x³ * x²= 22
x= 22
street light is at the top of a 19-ft-tall pole. a 6-ft tall woman walks away from the pole with a speed of 6 ft/sec along a straight path (see figure). how fast is the tip of her shadow moving, in ft/sec, when she is 50 ft from the base of the pole?
8.77 ft/sec is the tip of her shadow moving with a speed of 6 ft/sec .
What is speed, for instance?
Speed is the rate of change in location of an item, expressed in meters per second. If something starts at the origin and moves three meters in three seconds, for instance, its speed is one meter per second. The formula for speed is as straightforward as dividing a distance by a time.Let H = the height of the pole.
h = the height of the woman.
x = the length of the woman's shadow.
s = the distance from the pole to the woman.
By similar triangles, H/h = (s + x)/x or Hx = h(s + x).
Differentiating, H dx/dt = h(ds/dt + dx/dt)
19 dx/dt = 6(6 + dx/dt) = 36 + 6 dx/dt
13 dx/dt = 36
dx/dt = 36/13 ft/sec = 2.77 ft/sec for how fast her shadow is lengthening.
The speed of the tip of her shadow would be this speed added to her traveling speed: 2.77 + 6 = 8.77 ft/sec.
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15 POINTS HELP!
A liquid used to unclog sinks has a pH value of 14. This liquid is _____.
neutral
an acid
a base
Answer:
A base
Step-by-step explanation:
its not an acid bc a ph level of 14 means is has a strong base.
26% of all college students major in stem (science, technology, engineering, and math). if 36 college students are randomly selected, find the probability that a. exactly 7 of them major in stem. b. at most 10 of them major in stem. c. at least 7 of them major in stem. d. between 9 and 15 (including 9 and 15) of them major in stem.
The probabilities will be 0.1081 , 0.676, 0.863, 0.605 respectively.
let us consider, the chances of getting stem be a success(S) and not getting it be a failure(F) , and the total probability be 1 .
as per the statement 26% students are major in stem
total students selected randomly are 36.
∴ P(S) = 0.26
P( F) = 1 - 0.26 = 0.74
Now the binomial probability of success is given by
[tex]P(x) = C^{n} _{x} S^{x} F^{n-x}[/tex]
where C is for the combination formula
S is changes of success
F is chances of failure
x = no. of times success
n = total times the experiment done
From the provided information we can solve each case as follows :
A) exactly 7 of them major in stem
P(7) = [tex]C^{36} _{7} (0.26)^{7} (0.74)^{29}[/tex]
= 0.1081
B)at most 10 of them major in stem
it means P(0,1,2...10)
∴ P = P(0) + P(1) +......+P(10)
P = 0.676
C) at least 7 of them major in stem.
it means P(7,8,9...36)
∴ P = P(7) + P(8) + ...+ P(36)
P = 0.863
D) between 9 and 15 (including 9 and 15) of them major in stem.
In this case we subtract P(0,1,2...8) from P(0,1,2,...15)
and get P(9,10,11,...15)
∴ P(9,10,11,...15) = P(0,1,2,...15) - P(0,1,2...8)
= 0.987 - 0.382
= 0.605
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a school has 400 grade 9's, 375 grade 10's, 300 grade 11's and 325 grade 12's. twenty students from each grade are surveyed
The type of bias that can be present in stratified sampling is that the students cannot be selected to accurately reflect the population.
How are samples classified?Samples may be classified according to the five options as follows:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.In this problem, an equal amount of students from each class was surveyed, hence a stratified sample was used.
The type of bias present in stratified sampling is that the students cannot be selected to accurately reflect the population.
Missing InformationThe problem asks for which type of bias is present in this sample.
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when a certain unfair die is rolled, an even number is times as likely to appear as an odd number. the die is rolled twice. what is the probability that the sum of the numbers rolled is even?
The probability that the sum of the numbers rolled on the dice is even =1/2.
What is referred as probability?A probability is a measure of the magnitude of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages including several from 0% to 100% can be used to describe probabilities.For the given question,
A fair dice is rolled twice.
Six different results are available with a single roll of the dice (1,2,3,4,5,6)
Therefore, if two dice are rolled, there are a total of 36 possible results, or 6².
Sample space for the sum of even = [(1,1), (1,3), (1,5), (2,2), (2, 4),(2,6), (3, 1), (3,3),(3,5),(4,2),(4,4),(4,6), (5, 1), (5,3),(5,5),(6,2),(6,4),(6,6)]
Total sample space for sum of even = 18
For the probability that the sum of the numbers rolled is even is -
probability (sum is even) = 18 / 36 = 1/2
Thus, the probability that the sum of the numbers rolled is even is 1/2.
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Ms. Kirkland is baking muffins. Each batch of muffins uses 1 ½ pounds of flour. How many batches of muffins can she bake with 7 ½ pounds of flour? ______________ batches.
The number of batches of muffins Ms. Kirkland can bake with 7 ½ pounds of flour is 5 batches.
Given that, Ms. Kirkland is baking muffins. Each batch of muffins uses 1 ½ pounds of flour.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, [tex]1\frac{1}{2} = \frac{3}{2}[/tex] and [tex]7\frac{1}{2} = \frac{15}{2}[/tex]
The number of batches of muffins can she bake
= 15/2 ÷ 3/2
= 15/2 × 2/3
= 5 batches
Hence, the number of batches of muffins Ms. Kirkland can bake with 7 ½ pounds of flour is 5 batches.
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Answer: The answer is 5
Step-by-step explanation: I have my ways ;>
Pls help/ The y-intercept of f(x)=(1.6)x is ______________________ the y-intercept of the function in the graph:
The y-intercept of f(x) = (1.6)x is (a) less than the y-intercept of the function in the graph
How to complete the blank?The equation of the function is given as
f(x) = (1.6)x
To determine the y-intercept, we set x = 0
So, we have
f(0) = 1.6 * 0
Evaluate
f(0) = 0
For the graph, we have
When x = 0, the function has a value of 1
This means that
y-intercept is 1
0 is less than 1
Hence, the y-intercept of f(x) = (1.6)x is (a) less
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Part A Write a paragraph proof to prove ABC ≌ ABD. Explain in complete sentences each statement and reason. Be sure to give the reason the two triangles are congruent.
Part B Now that you have proven the two triangles are congruent, can you show that ∠CBA ≌ ∠DBA? Explain your reasoning in a complete sentence.
A. Both triangles have two pairs of corresponding sides and a pair of included angles, therefore, ΔABC ≌ ΔABD by SAS.
B. ∠CBA ≌ ∠DBA by CPCTC.
What is the SAS Congruence Theorem?The SAS congruence theorem state that if we have two triangles that we can show that they posses two pairs of corresponding sides that are equal and a pair of included angles that are also equal, then we can state that the two triangles are congruent to each other
When two triangles are proven to be congruent to each other, every corresponding parts of both triangles will be equal to each other based on CPCTC.
Part A:
We are given that AC ≌ AD, and ∠CAB ≌ ∠DAB.
Also, AB ≌ AB based on the reflexive property.
Therefore, both triangles are congruent to each other based on SAS.
ΔABC ≌ ΔABD
Part B:
Since both triangles are congruent, therefore ∠CBA ≌ ∠DBA by CPCTC.
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Write the equation of the line in fully simplified slope-intercept form.
ANSWER ASAP
WILL GIVE BRAINLIEST
The equation of the line in fully simplified slope - intercept form is 5x + 4y = 12 .
In the question ,
a graph of the line is given , we need to find the equation of the given line in the simplified slope - intercept form .
to find the equation , we need minimum two points ,
So , from the given graph ,
we can find that
when x [tex]=[/tex] 0 , the value of y [tex]=[/tex] 3 ,
the first point is (0 [tex],[/tex] 3) .
when x [tex]=[/tex] 4 , the value of y [tex]=[/tex] -2 ,
the second point is (4 [tex],[/tex] -2) .
the slope can be calculated by
slope = (-2-3)/(4-0)
= -5/4
So , the equation of the line passing through point (4,-2) with slope -5/4 , in the slope intercept form is
(y -(-2)) = (-5/4)(x-4)
y + 2 = (-5/4)x + 5
y = (-5/4)x + 5 - 2
y = (-5/4)x + 3
Simplifying further , we get
4y = -5x + 12
5x + 4y = 12
Therefore , The equation line in fully simplified slope - intercept form is 5x + 4y = 12 .
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T
4) a) On the grid, draw
the line y = 3
b) On the grid, draw
the line x = -2
6
5
4
-3-
2
1-
-3 -2 -1 0
-1-
-2
1
2
3
4
5
Fe
Be
1.
2.
3
4
Answer:
Step-by-step explanation:
Find the equation of the line that is parallel to another line whose equation is x+2y+8=0 and passes though the point(-2,-3)
There is no line parallel to the line x + 2 · y + 8 = 0, as point (x, y) = (- 2, - 3) lies on the original line.
How to determine the equation of a line parallel to another line and that passes through a given point.
In this problem we need to determine the equation of line based on its slope relationship respect to another line and a given point. Two lines are parallel if and only if they have the same slope (m) and two distinct intercepts (b). First, transform the given equation of the line into slope-intercept form:
x + 2 · y + 8 = 0
2 · y = - x - 8
y = - (1 / 2) · x - 4
Then, the resulting line has a slope of - 1 / 2.
Second, determine the intercept of the resulting line:
y = m · x + b
b = y - m · x
b = - 3 - (- 1 / 2) · (- 2)
b = - 3 - 1
b = - 4
The intercept of the resulting line is - 4.
Third, transform the equation of the resulting line into standard form:
y = - (1 / 2) · x - 4
- 2 · y = x + 8
x + 2 · y + 8 = 0
There is no parallel line for the point (x, y) = (- 2, 3).
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help meeeeeeeeeeeeeeeeee please
Answer:
324 ft
Step-by-step explanation:
[tex]v=\sqrt{2gh}[/tex]
[tex]v^2=(\sqrt{2gh})^2[/tex]
[tex]v^2=2gh[/tex]
[tex]\frac{v^2}{2g}=\frac{2gh}{2g}[/tex]
[tex]\frac{v^2}{2g}=h[/tex]
[tex]\frac{144^2}{2(32)}=h[/tex]
[tex]\frac{20736}{64}=h[/tex]
[tex]324=h[/tex]
Stacy is one-fourth as old as her mother. If Stacy's mother is 36, how old is Stacy?
Answer: Stacy is 12 years old
Step-by-step explanation:
36/4 = 12
What would the final cost be
for a trick or treat bucket that
originally costs $3.00 if you
have a coupon for 10% off and
you have to pay tax of 7.5%?
Answer:
4.73
Step-by-step explanation:
10% is 10
so, you have to multiple 3×.10=.30
3-.30=2.70
2.70×.75 because 7.5% is .75
that is 2.0250 and then you have to add 2.0250 with 2.70 that is 4.7250 and if you round it. It is 4.73
Hope that works
Can anyone write the equation of the graph?
The absolute equation in the graph is f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we can see that the lines on the graph has a sharp v-shape
Graphs that have this form are absolute value graphs
The general form of an absolute value equation is expressed as
y = |x - h| + k
From the above form, we have
Vertex = (h, k)
By definition, the vertex of a function is either the maximum point or the minimum point
On the given graph, the minimum point is (3, 5)
So, we have the following representation
(h, k) = (3, 5)
Substitute (h, k) = (3, 5) in the above equation
So, we have:
y = |x - 3| + 5
Hence, the function represented by the graph has an equation of f(x) = |x - 3| + 5
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Point B is graphed on the coordinate plane. Which ordered pair represents point B?
Which of these strategies would eliminate a variable in the system of equations?
2x + 8y = -3
3x + 6y = -4
A: Multiply the top equation by 333, multiply the bottom equation by -2−2minus, 2, then add the equations.
B: Multiply the top equation by 333, multiply the bottom equation by 444, then subtract the bottom equation from the top equation.
C: Multiply the top equation by -4−4minus, 4, multiply the bottom equation by 333, then add the equations
Option A: Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations will eliminate the variables.
Rewriting the equation -
2x + 8y = -3 : Equation 1
3x + 6y = -4 : Equation 2
Multiplying equation 1 with and equation 2 with -2.
6x + 24y = -9 : Equation 3
-6x - 12y = 24 : Equation 4
Adding the equation 3 and equation 4. This will eliminate the variable x.
12y = 15
y = 5/4
So, option 1 will eliminate the variable x on solving we get the value of y as 5/4.
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the probability that a single radar station will detect an enemy plane is 0.65. (a) how many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station? stations (b) if four stations are in use, what is the expected number of stations that will detect an enemy plane? (round your answer to one decimal place.)
If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-,
(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane?The expected number of sucesses of a binomial variable is given by:If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.learn more about probability click here:
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There are five people competing in the track meet this weekend. They are competing for 1st, 2nd, and 3rd place ribbons. How many different ways can the winners be chosen? A. 30 B. 60 C. 120 D. 150
If they are competing for 1st, 2nd, and 3rd place ribbons. The number of different ways can the winners be chosen is: B. 60.
How to find the total possibilities?Given data:
Number of people =5
Number of places = 1st, 2nd, and 3rd
Hence,
Different combinations =5 ×4×3
Different combinations = 60 ways
Therefore the winners will be chosen by 60 different possible ways ,
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