According to the question, the homeroom class wants to get a present for a student. From [tex]32[/tex]students, [tex]10[/tex] choose cards, [tex]12[/tex] choose t-shirts, [tex]6[/tex] choose a video and the remaining choose a bracelet.
Now, calculate the probability that the exchange students should get a card or a bracelet.
Let us assume, ‘C’ represents the card and ‘B’ represents the bracelet.
Using standard probability formula:
P (C or B) = P(C)+P(B) = [tex]\frac{10}{32} + \frac{4}{32} = \frac{14}{32} = \frac{7}{16} = 43.8%[/tex]
Therefore, the probability to get a card or a bracelet is [tex]43.8[/tex] percent.
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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solve 2xy - x = 3for y. Then find the value for y when x=2
solve 2y + xy = 6for y. Then find the value of y when x= -3
Answer:
1) y=5/4
2) y=−6
Step-by-step explanation:
Let's solve the equation step by step.
1) 2xy - x = 3
(2)(2)y - 2 = 3
4y - 2 = 3
4y−2=3
Step 1: Add 2 to both sides.
4y−2+2=3+2
4y=5
Step 2: Divide both sides by 4.
4y/4 = 5/4
y=5/4
2) 2y + xy = 6
2y−3y=6
Step 1: Simplify both sides of the equation.
2y−3y=6
2y+−3y=6
(2y+−3y)=6(Combine Like Terms)
−y=6
−y=6
Step 2: Divide both sides by -1.
−y/−1 = 6/−1
y=−6
Type the correct answer in the box. Use numerals instead of words.The graphs of functions fand g are shown.Function g is defined as g(x)
= k f(x). What is the value of K?
Answer:
k = 1
This is because when g(x) = 8, f(x) = 8
and when g(x) = 2, f(x) = 2
and this continues throughout the graph
What is the value of the digit in the thousands place?
5,963
OA. 900
OB. 300
O C. 5
OD. 5,000
Answer: D
Step-by-step explanation:
On the Math SAT, men have a distinct edge. In 2005, for instance, the men averaged about 538, and the women averaged about 504. You may assume (i) the histograms followed the normal curve, and (ii) both SDs were about 120. Estimate the percentage of men getting over 700 on this test in 2005.
The percentage of men getting over 700 on this test in 2005 is 8.85%.
How to calculate the value?It should be noted that based on the information illustrated, the percentage will be calculated thus:
= P(X - 538/120) > (700 - 538/120)
= P(Z > 1.35)
= 1 - P(Z <= 1.35)
Using normal table
= 1 - 0.9115
= 0.0885
Therefore, the percentage of men getting over 700 on this test in 2005 is 8.85%.
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Brian has $24 worth of pizza delivered to his house. He pays the bill plus a 15% tip and 7% sales tax. He also pays a 3$ delivery fee that is charged after the tax and tip how much change does he receive, if he pays with two $20 bills?
Pizza costing $24 is being delivered to Brian's home. The change $7.72 he get if he uses two $20 bills as payment.
Given that,
Pizza costing $24 is being delivered to Brian's home.
He pays the amount in addition to the 7% sales tax and 15% tip.
In addition, he pays the delivery price of $3, which is added on after tax and tip.
We have to find how much change does he get if he uses two $20 bills as payment.
To figure out the sales tax
$24×0.07=$1.68
To figure out the tip
$24×0.15=$3.6
The Total cost=$24+$1.68+$3.6+$3=$32.28
Now, To find change we have to add the Total cost and the bill
Change=2($20)-$32.28
Change=40-32.28
Change=$7.72
Therefore, The change $7.72 he get if he uses two $20 bills as payment.
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if 0 < x < 90 degrees and sin sin x = 5/13, what is tan x?
Step-by-step explanation:
If cos x = 5/13 and x is between 0 and 90 degrees, since we know that tan2x = sin2x/cos2x = (2 sinxcosx)/(cos^2x - sin^2x) and we are dealing with a 5-12-13 right triangle,
tan (2x) = 2(12/13)(5/13)/((5/13)^2 - (12/13)^2) = (2*12*5/13^2) / (25/13^2) - (144/13^2)= 120/(-119)= -1.008403
in a test designed to assess small motor coordination, kindergarten pupils are timed on their performance of a specific task. it is known that the time required to complete the task has an approximate bell-shaped distribution with mean 36 seconds and a standard deviation (s.d.) of 6 seconds. how long should the test administrator allow for the performance of the task, if it is desired that approximately 97.5% of the kindergarten pupils complete the task? question 16 options: 30 42 24 48
It would take the test administrator 48 seconds to allow for the performance of the task
So, if we want 97.5 percent, we must look it up in our z table. So I need to find the z score that is closest to.975, which is 1.96.
The 97.5th percentile point of the standard normal distribution is a quantity often used in probability and statistics for statistical computations. This figure is around 1.96, which means that 95% of the area under a normal curve is within 1.96 standard deviations of the mean.
As a result, the z score for the 97.5th percentile would be multiplied by the class standard deviation. As a result, we obtain;
1.96*6 = 11.76
Then, this new time gotten would be added to the first mean of the class,
As a result, we have 36+11.76 = 47.76 which is approximately 48
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The students in the astronomy club are selling snacks to raise money for a planetarium field trip. If they sell x muffins at $0.35 apiece and y bags of carrot sticks at $0.15 apiece, the total number of dollars raised will be T = 0.35x + 0.15y. How many dollars will they raise if they sell 210 muffins and 120 bags of carrot sticks?
Answer:
$91.5
Step-by-step explanation:
muffins: 210 carrot sticks:120
T= 0.35x + 0.15y (replace x as no. of muffins & y as no. of carrot sticks)
T= (0.35×210) + (0.15×120)
T= 73.5 + 18
T= 91.5
Draw ΔX Y Z and find the slope of each side of the triangle. Determine whether the triangle is a right triangle. Explain. X(0,0), Y(1, h), Z(2 h, 0)
A right-angled triangle is a triangle whose two adjacent sides form a right-angle triangle between them. The given triangle is a right-angled triangle.
What is a right-angle triangle?A right-angled triangle is a triangle whose two adjacent sides form a right-angle triangle between them.
The slope of the sides of the triangle can be written as,
The slope of XY = (2h - 0)/(2h - 0) = 1The slope of YZ = (0-2h)/(4h - 2h) = -2h/2h = -1The slope of XZ = (0 - 0)/(4h - 0) = undefined, therefore, the line will be horizontalThe given triangle is a right-angle triangle because the slope of the two lines is 1 and -1, whose product is -1. Therefore, the two lines are perpendicular to each other.
Hence, the given triangle is a right-angled triangle.
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what does ^3^ mean
please i dont know
Step-by-step explanation:
it looks like a smiley face
Which inequality is equivalent to I x-4 I <9
(B) –9 < x – 4 < 9 inequality is equivalent to Ix-4I <9.
What is inequality?Inequality is a statement of an order relationship between two numbers or algebraic expressions (greater than, greater than, or equal to, less than, or less than or equal to). Inequality is defined as a difference in size, amount, quality, social position, or another factor. Inequality occurs when you have ten of something and someone else has none. (mathematics) A statement stating that one quantity is less than (greater than) another.So, Ix-4I <9:
|x-4|<9 ⇒ -9 < x-4 < 9-5 < x < 13Therefore, (B) –9 < x – 4 < 9 inequality is equivalent.
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The complete question is given below:
Which inequality is equivalent to I x-4 I <9?
A –9 > x – 4 < 9
B –9 < x – 4 < 9
C x – 4 < –9 or x – 4 < 9
D x – 4 > –9 or x – 4 < 9
Find the sum of each finite series. Σ⁵ n=1(2 n-1)
The sum of the given finite series is 25
The summation notation means that we have to add the terms of the given series with n moves from the lower limit to the upper limit.
The given series is:
[tex]\sum\limits^5_{n=1} {(2n-1)}[/tex]
In this series, the lower limit is n = 1 while the upper limit is n=5.
n = 1 ⇒ 2n - 1 = 2(1) -1 = 1
n = 2 ⇒ 2n - 1 = 2(2) -1 = 3
n = 3 ⇒ 2n - 1 = 2(3) -1 = 5
n = 4 ⇒ 2n - 1 = 2(4) -1 = 7
n = 5 ⇒ 2n - 1 = 2(5) -1 = 9
Hence,
[tex]\sum\limits^5_{n=1} {(2n-1)}=1+3+5+7+9[/tex]
We can evaluate the sum of the series directly, or by using the sum formula as follow:
S(n) = n/2 [a(1) + a(n)]
Substitute n = 5, a(1) =1, and a(n) = 9:
S(5) = 5/2 (1 + 9) = 25
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1. A study is made to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration # 1, the reaction was run 15 times with an average velocity of 7. 5 micromoles per minutes and a standard deviation of 1. 5 with a substrate concentration #2, 12 runs were made, yielding an average velocity of 8. 8 micromoles per minutes and a sample standard deviation of 1. 2. Is there any reason to believe concentration #2 causes an increase in the mean velocity over concentration #1? use 0-0. 05 level of significance and assume the populations to be approximately normal distribution with equal variance. Instructions 1. Hypothesis.
There is not enough evidence
What is standard deviation ?An indicator of how much a group of numbers vary or are dispersed is the standard deviation. [1] When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.
For 1.5 moles substrate concentration per liter
Reaction ( n2 ) = 15 runs
average velocity ( x2 ) = 7.5 micromoles per 30 minutes
standard deviation ( s2 ) = 1.5
For 2.0 moles substrate concentration per liter
Reaction( n1 ) = 12 runs
(x1) = 8.8 micromoles on average per 30 minutes
standard deviation ( s1 ) = 1.2
Show Reason to believe that this increase in substrate conc causes an increase in mean velocity
Hypothesis test
H0 : μ1 - μ2 = 0.5
H1 : μ1 - μ2 > 0.5
significance level ( ∝) = 0.01
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Tisha's class is having a gift exchange. Tisha will draw first and her friend Brandi second. If there are 18 students participating, what is the probability that Brandi and Tisha draw each other's names?
According to the question, in the gift exchange event. Tisha draws first gift and her friend Brandi second gift.
The total number of participating students is [tex]18[/tex].
To calculate the probability that Brandi and Tisha draw each other’s name is as follows:
Using conditional probability, the solution is as follows:
[tex]P(E) = \frac{1}{18}\frac{1}{17} = \frac{1}{306} = 0.3%[/tex]
The calculated percentage is [tex]0.3[/tex].
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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A dishwasher is priced at $475 there are two options offered to reduce the price either a 15% discount off the price or a rebate of $75 which is the better choice and what is the extra amount saved
Answer:
The better choice is a rebate of $75. You would save $3.75 more.
what statement best defines an angle
Evaluate each expression 10+8^3 divid 16
Answer:
42
Step-by-step explanation:
= 10+8^3/16
= 10+512/16
= 10+32
= 42
Samra's guardians invested money for her into a 529 College Savings Plan, which compounds annually. The growth of the savings plan per year, x, can be represented by the exponential function f(x) = 500(1.03)x. What is the meaning of the y-intercept in the context of the problem?
A. The percent rate of change is 500%.
B. The initial value of the investment is $500.
C. The principal amount put into the savings plan is $1.03.
D. The average rate of change that is occurring is 1.03.
In the context of this problem, the meaning of the y-intercept is: D. The average rate of change that is occurring is 1.03.
What is the average rate of change?The average rate of change can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.
In Mathematics, the y-intercept of any graph occurs at the point where the value of "x" is equal to zero (0). Similarly, the x-intercept refers to the point at which the graph of a function crosses the x-axis and the value of "y" is equal to zero (0).
In the context of this problem, we can reasonably infer and logically deduce that the meaning of the y-intercept is the average rate of change that is occurring is 1.03 while 500 represents the initial investment.
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Explain what it means for a sequence to be an arithmetic sequence.
Any sequence is termed as the arithmetic sequence when the common difference between two consecutive values are same.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between the two numerical orders is a fixed value (AP). Arithmetic Sequence is another name for it.
We'd come across a few particular words in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be defined in concepts of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, for the given question;
Let the initial term be 'a₁'.
Let the second term be 'a₂'.
Let the third term be 'a₃'.
And, consider the fourth term as 'a₄'.
The AP must have the equal common difference. So,
d = a₃ - a₂ or d = a₄ - a₃
When the value of the common difference 'd' is found same in any of the cases, it said to form an AP.
Therefore, for the sequence to be an arithmetic sequence in common difference must be equal.
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Triangles ABC and DEF are mathematically similar.
A
9 cm
6/44
B
The area of triangle ABC is 34 cm².
Calculate the area of triangle DEF.
A
F
13.5 cm
E
Triangles ABC and DEF are mathematically similar. The area of triangles ABC is 34cm^2. Calculate the area of triangle DEF from the picture.
The required Area of Triangle DEF is 51cm square.
Given that,
The triangles ABC=DEF
Then, height of ABC= height of DEF
By the given picture we have
CB = 9cm
FE =13.5cm
Area of ABC= 34cm square
According to the question,
The area of a triangle= [tex]\frac{1}{2}[/tex] × base × height,
Again, Area of ABC = [tex]\frac{1}{2}[/tex] × base × height= 34cm square
= [tex]\frac{1}{2}[/tex] × 9cm × height= 34cm square
= [tex]\frac{9}{2}[/tex] cm × height= 34cm square
= Height= [tex]\frac{34cmsquare}{\frac{9}{2} }[/tex]
= Height = [tex]\frac{68}{9}[/tex]cm.
The height of the triangle ABC is [tex]\frac{68}{9}[/tex]cm.
Therefore,
Area of DEF = [tex]\frac{1}{2}[/tex] × base × height
= [tex]\frac{1}{2}[/tex] × 13.5cm × ([tex]\frac{68}{9}[/tex])cm
= 51cm square
Therefore, the Area of Triangle DEF is 51cm square.
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Oscar wants to rent a boat. Boats 4 Less charges a fee of $100 and $35 per hour after that. Boats-R-Us doesn't charge a fee but charges $50 per hour. If Oscar wants to rent the boat for 8 hours, which rental company should he use and why?
(P.S. This has to do with Linear Equations so figure out which form to use Point-Slope From, Slope Intercept Form or Standard Form)
The rental company to hat Oscar should use is the second company because it's cheaper.
How to illustrate the information?The total amount charged for the first boat will be:
= 100 + 35h
where h = number of hours
= 100 + 35(8)
= 100 + 260
= $360
The amount charged for the second company will be:
= 50 × 8
= 400
Therefore, the rental company to hat Oscar should use is the second company because it's cheaper.
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Find the missing term(s) of each arithmetic sequence. 1, □, 9,. . . . .
Missing term i.e., the second term of the sequence is 5.
As the series is in an arithmetic sequence, so we have an equation
[tex]a_{n}[/tex] = a +(n-1)d
Where a = first number of the series
n = number of term
d= common difference
As we know the 3rd term of the sequence, so by this we can find the common difference.
So we have,
9 = 1 +(3-1)d
8=2d
d=4
common difference = 4
Now we have to find the 2nd term or the missing term of the sequence, so we have
[tex]a_{2}[/tex] = 1 +(2-1)4
= 1+ 1×4
= 1+4
= 5
Therefore the 2nd term is 5.
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There are 130 people in a sport centre. 73 people use the gym. 62 people use the swimming pool. 58 people use the track. 22 people use the gym and the pool. 29 people use the pool and the track. 25 people use the gym and the track. 11 people use all three facilities. how many people use at least two facilities? check skip do not use a calculator get help report a mistake to hegartymaths on-screen keypad on off 789qwertyui
Using Venn diagram, out of the 130 people in the sport center, 54 people use at least two facilities.
Venn diagram is a diagram used to present the relationship between sets in a logical form. (See attached image)
Let n = number of people who use at least two facilities
A = people who use the gym = 73
B = people who use the swimming pool = 62
C = people who use the track = 58
A ∩ B = 22
B ∩ C = 29
A ∩ C = 25
A ∩ B ∩ C = 11
n = (A ∩ B - A ∩ B ∩ C) + (B ∩ C - A ∩ B ∩ C) + (A ∩ C - A ∩ B ∩ C) + A ∩ B ∩ C
n = (22 - 11) + (29 - 11) + (25 - 11) + 11
n = 11 + 18 + 14 + 11
number of people who use at least two facilities = 54
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Directions:Add. Express The answer in simplest form. show all necessary work -2 2/3 - 7 1/3
Answer:
-10
Step-by-step explanation:
Convert to improper fractions and do the math
-8/3 - 22/3
-30/3
-10
Kevin is 6 years older than Timothy. 4 years ago, Kevin was twice as old as Timothy. Find their present ages.
Answer:
k=12
t=8
Step-by-step explanation:
two equations from the question
1 k=t+6
2 (k-4)=(t-4)×2
develop these
3. k-4=2t-8
4. 2 times first equation
2k=2t+12
subtract 4 from 3
-k-4=-20
k=16
sub back in
t=10
By rounding to 1 significant figure, estimate
174.2 x 23.46
162.9 x 10.73
By rounding to 1 significant figure is 2.
What is significant figures ?Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value The first non-zero digit is where we start counting significant figures. The first non-zero digit of a number is considered the first significant figure when counting significant figures. The second digit is considered the second significant figure, and so on. The decimal point may be followed by a significant figure to the left or right of it.
Given: ([tex]\frac{(174.2 × 23.46)}{162.9 × 10.73}[/tex])
174.2 × 23.46 = 4086.732
162.9 × 10.73 = 1747.917
[tex]\frac{4086.732}{1747.917}[/tex] = 2.338 (approx)
= 2 ( rounding to 1 significant figure )
Hence the rounding to 1 significant figure is 2.
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HELP FAST i'll mark you brainliest please.
The transformation of the given function g(x) = ¹/₂|x + 4| - 3 using the format h(x) = a|bx + c| + d, gives;
a = ¹/₂
b = -1
c = 6
d = 3
How to carry out Transformation of functions?
We are given the function;
g(x) = ¹/₂|x + 4| - 3
Now, we are told that the function is first translated by 6 units upwards, and so this means a transformation of;
g(x) + 6 = ¹/₂|x + 4| - 3 + 6
g'(x) = ¹/₂|x + 4| + 3
Now, we are told that it now undergoes a transformation of 2 units to the right, this gives;
g"(x) = ¹/₂|x + 4 + 2| + 3
g"(x) = ¹/₂|x + 6| + 3
Finally, after undergoing a transformation of reflection in the y-axis, we have; h(x) = ¹/₂|-x + 6| + 3
For the format of;
h(x) = a|bx + c| + d, it means that we have;
a = ¹/₂
b = -1
c = 6
d = 3
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Solve for x.
-3/8x-7/24x+1/3x=-40
Answer:
120
Step-by-step explanation:
We start with the equation:
[tex]\frac{1}{3}x-\frac{3}{8}x -\frac{7}{24}x =-40[/tex]
We need to set the fractions into equal denominations so we can sum them all together:
[tex]\frac{8}{24}x-\frac{9}{24}x -\frac{7}{24}x =-40\\[/tex]
Now sum the fractions:
[tex]\frac{8-9-7}{24}x=-40\\\\ \frac{-8}{24}x=-40[/tex]
Multiple both sides by 24 to eliminate denominator on left side of equation:
[tex]-8x=-960[/tex]
Divide both sides by -8 to get the value of x:
[tex]x=120[/tex]
Solve y3 = −8.
please helpp
Answer:
-2
Step-by-step explanation:
Cube root of eight is 2
y= -2
Choose an equation for the relationship between the measures of the angles and arcs.
1 and the intercepted arcs and ________.
m1 = (m + m)
m1 = (m - m)
m1 = m + m
The expression that relates the measure of <1 and arcs QP and arcSP is expressed as m<1 = 1/2(arcQR+arcSP)
Circle theoremWhen two chords intersect inside a circle, the angle formed is half of the sum of the subtended arcs.
From the given diagram, the intercepted arcs are arcQR and arcSP and the measure of the interior angle is <1.
Using the theorem above, the expression that relates the measure of <1 and arcs QP and arcSP is expressed as:
m<1 = 1/2(arcQR+arcSP)
The measure of the angle <1 is equivalent to half the sum of arcQR and arcSP.
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