The probability that Robert picks a black marble is 3/8. The result is obtained from the ratio of the number of black marble to all marbles.
What is probability?Probability is a numerical description of how possible an event to happen. Tha value of probability is between 0 to 1. Zero probability means something is impossible to happen. Probability 1 shows certainty.
Probability of an event can be expressed as
P(A) = n(A) / n(S)
Where
P(A) is the probability of an event An(A) is the number of favorable outcomesn(S) is the total number of events in the sample spaceIn case Robert has 3 black marbles and 5 marbles of other colors, then he picks a marble randomly, what is the probability of picking black marble?
Total number of marbles is 3 + 5 = 8.
n(S) = 8
Number of black marble is 3.
n(A) = 3
The probability of picking black marble is
P(A) = n(A) / n(S)
P(A) = 3/8
Hence, the probability that Robert picks a black marble is 3/8.
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Does anybody know the answer to this question?
The values of x and y after solving the given system of equations are respectively.
According to the question,
We have the following two equations:
y = 2x+3 ....(1)
y = 4x-1 .....(2)
Now, we can put the value of y from equation 1 in equation 2:
2x+3 = 4x-1
Now, we can change sides as it will not affect the result.
4x-1 = 2x+3
Moving 2x from the right hand side to the left hand side will result in the change of sign from plus to minus:
4x-2x-1 = 3
2x-1 = 3
2x = 3+1
2x = 4
x = 4/2
x = 2
Now, we can put the value of x in equation 1 to find the value of y:
y = 2x+3
y = 2*2+3
y = 4+3
y = 7
Hence, the value of x is 2 and the value of y is 7 after solving the equations.
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Divide 7 and 2 over 3 ÷ negative 3 and 1 over 5.
negative 2 and 19 over 48
negative 24 and 8 over 15
negative 21 and 2 over 15
negative 3 and 19 over 93
Dividing 7 and 2 over 3 ÷ negative 3 and 1 over 5 will give a quotient of negative 2 and 19 over 48
How to determine the quotient of 7 and 2 over 3 ÷ negative 3 and 1 over 5information gotten from the question include
Divide 7 and 2 over 3 ÷ negative 3 and 1 over 5.
Division is a basic mathematical operator that performs the function of sharing
division of fraction is done as follows
7 and 2 over 3
= 7 2/3
= 23/3
negative 3 and 1 over 5.
= -3 1/5
= -16/5
= 23/3 ÷ -16/5
= 23/3 * -5/16
= -115/48
= -2 19/48
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if p || , m<7 = 131°, and m<16 = 88°, find the measure of the missing angle m<4= ?
According to the theorem, the corresponding angles, formed by a transversal on a pair of parallel sides, are always equal.
Also, the sum of angles on a straight line is 180 degree.
The angles 5 and 7 constitute a pair of corresponding angles, formed by the transversal 'r' on the pair of parallel sides 'p' and 'q'. So they must be equal,
[tex]\begin{gathered} \angle5=\angle7 \\ \angle5=131^{\circ} \end{gathered}[/tex]The angles 4 and 5 constitute a straight line, so they must add up to be 180 degrees,
[tex]\begin{gathered} \angle4+\angle5=180^{\circ} \\ \angle4+131^{\circ}=180^{\circ} \\ \angle4=180^{\circ}-131^{\circ} \\ \angle4=49^{\circ} \end{gathered}[/tex]Thus, the angle 4 measures 49 degrees.
State which graph would most appropriately represent the given situation
Since we are measuring bank preference, we want to see the data in order of importance, then, the pareto chart is the most useful graph in this situation
X=
////////////////////////////
Answer: [tex]x=15[/tex]
Step-by-step explanation:
By the consecutive interior angles theorem,
[tex]150+3x-15=180\\\\3x-15=30\\\\3x=45\\\\x=15[/tex]
Currently Madeline makes $28,800 a year. Based on the following list ofmonthly expenses, find Madeline's adjusted monthly income (AMI).Student Loan:$250 (5 years remaining)Car Loan:$180 (6 months remaining)Personal Loan:$150 (30 months remaining)Apartment Lease: $425 (4 months remaining)>Gas/Electric:~$115 each month
Given:
yearly salary=28,800
Required:
To calculate adjusted monthly income
Explanation:
student loan
250 dollar
I need this answer asap!! Taylor earned $338.00 at her job when she worked for 20 hours. What was her hourly wage, in dollars per hour?
Answer:
$16.90 per hour
Step-by-step explanation:
You want the hourly wage Taylor earned when she worked 20 hours for $338.00.
Hourly wageTo find dollars per hour, divide dollars by hours:
$338.00/(20 h) = $16.90/h
Taylor earned $16.90 per hour.
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A line passes through the points (-18, -2) and (9, 10). Find this line's equation in point-slope form. Using the point (-18, -2), this line's point-slope form equation is [ ]Using the point (9, 10), this line's point-slope form equation is [ ]
We know that the point-slope formula is given by:
y − y₁=m(x − x₁)
where the terms: m, y₁ and x₁ are numbers.
Given that the line passes through a given points we have that:
m is the slope of the line
y₁ is the y value of that given point
x₁ is the x value of that given point
Finding the slopeWe want to find the slope m, having that
(x₁, y₁) = (-18, -2)
(x₂, y₂) = (9, 10)
The slope is always a rate of change. It is:
m = Δy/Δx,
where Δ means "change"
Step 1: finding the change of each term x and y
Δy = change of y = y₂ - y₁
Δy = 10 - (-2) = 12
Δx = change of x = x₂ - x₁
Δx = 9 - (-18) = 27
Step 2: dividing the found quantities
Then
m = Δy/Δx = 12/27
m = 4/9
Step 3: replacing in the equation
Using the equation, we have that
y − y₁ = m(x − x₁)
replacing m:
y − y₁= 4/9(x − x₁)
Step 4: replacing each pointFor the first point: (-18, -2)
We have that (x₁, y₁) = (-18, -2)
since the equation is
y − y₁ = 4/9(x − x₁)
replacing each term for each number of the given coordinate
y − (-2) = 4/9(x − (-18))
y + 2 = 4/9(x + 18)
Equation: y + 2 = 4/9(x + 18)
For the second point: (9, 10)
We have that (x₂, y₂) = (9, 10)
since the equation is
y − y₂ = 4/9(x − x₂)
replacing each term for each number of the given coordinate
y − (10) = 4/9(x − (9))
y - 10 = 4/9(x - 9)
Equation: y - 10 = 4/9(x - 9)
What two numbers multiplied give you 100 and added give you 21?
Answer: [tex]\frac{21}{2}+\frac{\sqrt{41}}{2}, \frac{21}{2}-\frac{\sqrt{41}}{2}[/tex]
Step-by-step explanation:
Let the two numbers be x and y.
[tex]x+y=21 \implies y=21-x\\\\xy=100\\\\\therefore x(21-x)=100\\\\21x-x^2 =100\\\\x^2 -21x+100=0\\\\x=\frac{21 \pm \sqrt{21^2 -400}}{2}=\frac{21}{2} \pm \frac{\sqrt{41}}{2}[/tex]
(-25)^(/3) =?-125 1 O A. -25 B. 5 or -5 C. -15 D. -5
We will have that the expression has the solution of:
[tex]\sqrt[3]{-125}=-5[/tex]Therefore the solution is D. -5.
When we elevate to the power of 3 -5 will be equal to -125.
Determine whether a triangle can have the following sides with the given lengths
For the length to be sides of a triangle, the sum of any two sides triangle must be greater than third side.
[tex]\begin{gathered} 19+5>15 \\ 24>15 \end{gathered}[/tex]Condition is true.
[tex]\begin{gathered} 15+5>19 \\ 20>19 \end{gathered}[/tex]Condition is true.
[tex]\begin{gathered} 19+15>5 \\ 34>5 \end{gathered}[/tex]Condition is true.
The triangle inequality satisfied for the triangle. So length belongs to a side of triangle.
Answer: yes
Which inequality represents the graph?
y less than negative one-fourth (x minus 10) squared + 4
y greater than negative 4 (x + 10) squared + 4
y greater than one-fourth (x minus 10) squared + 4
y greater than 4 (x + 10) squared + 4
Answer: 1st option!
Step-by-step explanation:
Just did it on edg
Help really need it
.........................................
Answer:
you wmekekd
Step-by-step explanation:
Factor Pairs (MAJOR POINTS!)
Answer:
3rd option
Step-by-step explanation:
the factors of 48 are
1 , 2, 3, 4, 6, 8, 12, 16 , 24 , 48
the factor pairs are
1 × 48 , 2 × 24 , 3 × 16 , 4 × 12 , 6 × 8
Mamadou spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7325 feet. Mamadou initially measures an angle of elevation of 15 degrees to the plane at point A. At some later time, he measures an angle of elevation of 42 degrees to the plane at point BB. Find the distance the plane traveled from point AA to point BB. Round your answer to the nearest foot if necessary.
The distance between points A and B will be 19201.93 feet.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
Mamadou notices an airplane arriving in a straight line and flying directly overhead on the radar. The plane stays at the same height of 7325 feet. Mamadou initially measures a 15-degree angle of inclination to the plane at point A. Later, he detects a 42-degree angle of elevation to the plane at point B.
The distance between points A and B will be given as,
D = 7325 / tan 15° - 7325 / tan 42°
D = 27337.27 - 8135.34
D = 19201.93 feet
The distance between points A and B will be 19201.93 feet.
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Answer:
19202 feet
Step-by-step explanation:
I got the same problem and got it right with that answer.
six distinct positive integers are randomly chosen between and , inclusive. what is the probability that some pair of these integers has a difference that is a multiple of ?
Answer:
So the probability of this happening is exactly 1 - it must be true
Step-by-step explanation:
If we calculate modulo(5) for each of the six numbers (the integer remainder after dividing by 5), we will get six values from 0 to 4.
By the pigeonhole principle, since there are 6 numbers and only 5 possible values, at least two must share the same value modulo 5. Pick two of those, say x and y, in which case x mod 5 = y mod 5, therefore (x - y) mod 5 = 0. In other words, their difference is a multiple of 5.
So the probability of this happening is exactly 1 - it must be true
a researcher counted the hours a brand of batteries could power different devices. the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. what percentage of devices ran on the batteries for fewer than
the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. So 10.2% of gadgets were powered by batteries for fewer than 63 hours.
Given that,
Data have a mean of 74.6 hours and a standard deviation of 9.1 hours, and they are regularly distributed.
The standard deviation is defined as ?
The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
[tex]p(X\leq 63) = p(Z\leq 63-74.6/9.1)[/tex]
From standard deviation,
[tex]p(X\leq 63) = p(Z\leq -1.279)= 0.1061[/tex]
a certain percentage of gadgets have battery life of less than 63 hours.
X= 63 hours
Percentage of devices ran on the batteries for fewer than 63 hours = 10.2%
Therefore, 10.2% of electronic devices had battery life of less than 63 hours
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f(x)=|x+3| vertical stretch by factor of 4
The image of the function after it is vertically stretched is f'(x) = 4|x + 3|
How to determine the equation of f(x) after the transformation?The function is given as
f(x) = |x + 3|
The transformation is given as
Vertical stretch by a factor of 4
This implies that we stretch the function f(x) by a factor of 4
This transformation is represented mathematically as
(x, y) = (x, 4y)
So, we have
f'(x) = 4 * f(x)
So, we have the following equation
f'(x) = 4 * (|x + 3|)
Remove the bracket
So, we have
f'(x) = 4 * |x + 3|
Evaluate the products
So, we have
f'(x) = 4|x + 3|
Hence, the equation of f'(x) is f'(x) = 4|x + 3|
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P(x) = x³- 2x² + 5x.
factor p completely
Answer:
P(x) = x (x²- 2x + 5)
Step-by-step explanation:
First factor x out:
P(x) = x (x²- 2x + 5)
Then, try to simplify (x²- 2x + 5):
However, there is no way to further simplify.
So, the answer should be x (x²- 2x + 5).
what is 1.025 as a fraction?
The decimal number 1.025 is 41/40 in fractions.
What is Number system?A number system is defined as a system of writing to express numbers.
A fraction is a part of a whole
The decimal number one point zero two five should be converted to fraction.
The conversion of 1.025 to fraction is 41/40.
If we calculate 41/40 we get the value 1.025.
Hence 1.025 is 41/40 in fractions.
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Quadrilateral ABCD is dilated with center
( 0, 0 ), taling B to B' . Draw A' B' C' D' .
Answer:
See the picture below
Step-by-step explanation:
an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 280280 engines and the mean pressure was 6.86.8 lbs/square inch. assume the standard deviation is known to be 0.90.9. if the valve was designed to produce a mean pressure of 6.76.7 lbs/square inch, is there sufficient evidence at the 0.050.05 level that the valve does not perform to the specifications? state the null and alternative hypotheses for the above scenario
We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is significantly lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.05 and observe that p'.
What is the meant by hypothesis test?Hypothesis test: A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters thanks to hypothesis testing.
Data are provided and noted.
X=6.8 display the sample mean
σ= 0.9 show the population's standard deviation.
n= 280 samples taken
μο=6.7 the value that we wish to test should be represented
α=0.1 signify the hypothesis test's level of significance.
The stat would be represented as z. (variable of interest)
p' indicate the test's p value (variable of interest)
Name the prevailing and competing hypothesis
The system of hypothesis must be tested to see if the true mean is below the criteria.
Null hypothesis: μ ≥ 6.7
Alternative hypothesis: μ < 6.7
Applying a z test to compare the actual mean to the reference value is preferable if the sample size is greater than 30 and we are aware of the population variation. The statistic is given by:
z=(X-μο)/σ[tex]\sqrt{n}[/tex] ......(1)
z-test: "enables the comparison of group means. One of the most widely used tests, it is used to determine whether the mean is (higher, lower, or not equal) to a given value ".
Calculate the statistic
We can replace in formula (1) the info given like this:
z=(6.8-6.7)/0.9[tex]\sqrt{280}[/tex]
P-value
Since is a one sided test the p value would be:
p'=p(z<0.0066)
We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is considerably lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.1 and observe that p'.
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What is the inequality shown? -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 O 5 6 7 8 9 n
Answer:
Inline range: 2 ≤ n < 8
Interval range: [ - 2, 8 )
Loop: n = - 2; n < 8;
Step-by-step explanation:
The filled circle means inclusive while outlined circle means exclusive.
Answer:
-2 ≤ x > 8
Step-by-step explanation:
x = a possible number based on the diagram
the black-filled-in dot on the line above the number line indicated that it can either be '≤' or '≥'
the empty-not-filled-in dot means that it can be either '<' or '>'
the '≤' means x can be equal or greater to -2
and the '>' means that x must be less than 8
hope this helps!
the number of lightning strikes on a square kilometer of open ground in a year has mean 6 and standard deviation 2.4. (these values are typical of much of the united states.) the national lightning detection network uses automatic sensors to watch for lightning in a sample of 25 randomly chosen square kilometers. what are the mean and standard deviation of the mean number of strikes per square kilometer?
The mean and standard deviation are given as 6 and 0.48 respectively.
According to the question The Population Mean number of strikes per square kilometer (μ) = 6 and the Population standard deviation of strikes per square kilometer (σ) = 2.4. The Sample size is equal to (n) = 16. We know that the sample mean number of strikes per square kilometer (m) = mean Number of strikes per square kilometer in the population. From this observation it is clear that the mean will be equal to
μ = m = 6
So, the Sample mean = 5
Now, the Standard deviation = standard error = σ/√n. Now we get
Standard Error = 2.4 / √25
Standard Error = 2.4 / 5
Standard Error = 0.48
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Ben earned 625.5 points out of 700 on an essay and 65out of 70 on an assignment. In order to earn an A in theclass, he needed to average a 91 on these twoassignments. Did Ben earn an A?
We were told that Ben earned 625.5 points out of 700 on an essay. Expressing his score in the essay in terms of percentage, it becomes
625.5/700 x 100 = 89.29%
Also, he scored 65 out of 70 on an assignment. Expressing his score in the assignment in terms of percentage, it becomes
65/70 x 100 = 92.86%
We would find the average between the two percentages
Average = sum of percentages/number of percentages
Average = (89.29 + 92.86)/2
Average = 91.075
Average is approximately 91%
Since in order to earn an A in the class, he needed to average a 91 on these two
assignments and he got an average of 91%, then we can conclude that he got an A
Complete the equation of the line through (-6,-5)(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and (-4,-4)(−4,−4)left parenthesis, minus, 4, comma, minus, 4, right parenthesis.
The equation of line that passes through the points (-6,-5) and (-4,-4) is x - 2y = 4 .
The equation of the line passing through the points (x₁,y₁) having slope as m is given by the formula .
y-y₁ = m(x-x₁)
In the question ,
it is given that
the required line passes through the points (-6,-5) and (-4,-4) ,
So , the slope(m) is = (-4 -(-5)/(-4 -(-6))
= (-4+5)/(-4+6)
= 1/2
the equation of the line passing through (-4,-4) and slope as 1/2 is
(y -(-4)) = (1/2)(x -(-4))
y + 4 = (x+4)/2
2y + 8 = x + 4
x - 2y = 8-4
x - 2y = 4
Therefore , The equation of line that passes through the points (-6,-5) and (-4,-4) is x - 2y = 4 .
The given question is incomplete , the complete question is
Complete the equation of line that passes through the points (-6,-5) and (-4,-4) .
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Use the information on the diagonal to find: a. the length ACb. the length ABc. the perimeter of quadrilateral ABCDd. the area of quadrilateral ABCD
A) To find the length AC, we must use the trigonometric ratio
[tex]\cos \text{ 31 =}\frac{adjacent}{hypothenuse}[/tex]adjacent = 5cm
hypothenuse = AC
[tex]\begin{gathered} \cos 31\text{ = }\frac{5}{AC} \\ AC\text{ = }\frac{5}{\cos 31} \\ AC\text{ =}5.8332\operatorname{cm} \end{gathered}[/tex]B) To find the length AB, we will use the value of AC just obtained to get it
since triangle ABC is a right-angled triangle, we will use Pythagoras theorem
so that
|AC|^2 = |AB|^2 +|BC|^2
AC = 5.8332cm
BC = 4cm
|AB|^2 = |AC|^2 - |BC|^2
[tex]\begin{gathered} AB\text{ = }\sqrt[]{5.8332^2-4^2} \\ AB\text{ = }\sqrt[]{18.0262224} \\ AB\text{ = 4.245729883cm} \end{gathered}[/tex]C) The perimeter of the quadrilateral can be found by adding the length of all the sides around its edges.
Perimeter = AD +CD + BC + AB
We do not have CD and we must find CD
[tex]\begin{gathered} CD\text{ = }\sqrt[]{|AC|^2-|AD|^2} \\ CD\text{ =}\sqrt[]{5.8332^2-5^2} \\ CD\text{ =}\sqrt[]{9.02622224} \\ CD\text{ = 3.004366195cm} \end{gathered}[/tex]Perimeter of ABCD = 5 + 3.004366195 + 4 +4.245729883 = 16.25009708cm
D) To find the area of the quadrilateral we must find the area of triangle ADC and triangle ABC.
Area of triangle ADC = 1/2 x base x height= 1/2 x 3.004366195 x 5 = 7.510915488 square centimeter
Area of triangle ABC = 1/2 X base x height = 1/2 x 4 x 4.245729883 =8.491459766 square centimeter
Area of quadrilateral ABCD = 7.510915488 + 8.491459766 = 16.00237525 square centimeter
can you help mw with my work?
In this problem the function that models the hight is:
[tex]h(t)=-5t^2+14t+3[/tex]So when the water hits the grownd h=0 so we replace that and solve for t so:
[tex]0=-5t^2+4t+3[/tex]To solve this expression we can use the cuadratic equation:
[tex]x=\frac{-4\pm\sqrt[]{16-4(-5)(3)}}{-10}[/tex]and we operate so:
[tex]\begin{gathered} x=\frac{-4\pm\sqrt[]{76}}{-10} \\ x=\frac{-4\pm8.7}{-10} \end{gathered}[/tex]Now we solve bout of the equation so:
[tex]\begin{gathered} x_1=\frac{-4+8.7}{-10}=-0.47 \\ x_2=\frac{-4-8.7}{-10}=1.27_{} \end{gathered}[/tex]So the answer that have sense is the secon one so the water hits the ground after 1.27 seconds
What is 25% of 130? Round to one decimal place ___________
Answer:
32.5
Step-by-step explanation:
What is 25% of 130?
0.25 * 130 = 32.5
Select which of these transformations is hardest for you to write using algebraic notation.
The graph that is hardest to write the transformation using algebraic notation is the second top graph counting from left to right
What are graph?A graph is a pictorial representation of data
What is transformation?A transformation is a movement that can be represented in a cartesian plane.
There several types of movement involved in transformation, some of them are:
TranslationReflectionDilation and so onThe first top graph counting from the left is a translation to the left.
The first graph at the bottom counting from the left is a translation downwards
The next bottom graph is reflection along x axis and translation downwards
The most difficult which is the second at the top counting from left involves dilation.
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