Answer:
The total price before discount was £63.
The price of the watch before discount was £25.
Step-by-step explanation:
Let the total original price before discount be x.
The total of £53.55 included a 15% discount. That means he paid only 85% of the original total price before the discount.
85% of x = £53.55
0.85x = 53.55
x = 63
The total before discount was £63.
£63 - £38 = £25
The total price before discount was £63.
The price of the watch before discount was £25.
In the triangles below, m B = MZP and mZT = m J.
What is the length of PQ?
6
3
5
12
I can't solve it because it didn't have enough information
A container holds less than 4 gallons of paint. Which inequality represents q, the number of quarts of paint it can hold? Recall that 4 quarts equal 1 gallon. A. q 1 C q 16
Answer:
q<16
Step-by-step explanation:
Multiply four quarts by four gallons. This gives us 16. Now, since it says less than, and not less than or equal to, we use < symbol. q<16
Answer:
q<16
Step-by-step explanation:
Suppose ARB Bank is reviewing its service charges and interest payment policies on current accounts. Suppose further that ARB has found that the average daily balance on personal current accounts is GH¢350.00, with a standard deviation of GH¢160.00. In addition, the average daily balances have been found to follow a normal distribution;
What percentage of customers carries a balance of GH¢100 or lower?
What percentage of customers carries a balance of GH¢500 or lower?
What percentage of current account customers carries average daily balances exactly equal to GH¢500?
What percentage of customers maintains account balance between GH¢100 and GH¢500?
Answer:
5.94% of customers carries a balance of GH¢100 or lower.
82.64% of customers carries a balance of GH¢500 or lower.
0% of current account customers carries average daily balances exactly equal to GH¢500.
76.7% of customers maintains account balance between GH¢100 and GH¢500
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 350, \sigma = 160[/tex]
What percentage of customers carries a balance of GH¢100 or lower?
This is the pvalue of Z when X = 100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 350}{160}[/tex]
[tex]Z = -1.56[/tex]
[tex]Z = -1.56[/tex] has a pvalue of 0.0594
5.94% of customers carries a balance of GH¢100 or lower.
What percentage of customers carries a balance of GH¢500 or lower?
This is the pvalue of Z when X = 500.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{500 - 350}{160}[/tex]
[tex]Z = 0.94[/tex]
[tex]Z = 0.94[/tex] has a pvalue of 0.8264
82.64% of customers carries a balance of GH¢500 or lower.
What percentage of current account customers carries average daily balances exactly equal to GH¢500?
In the normal distribution, the probability of finding a value exactly equal to X is 0. So
0% of current account customers carries average daily balances exactly equal to GH¢500.
What percentage of customers maintains account balance between GH¢100 and GH¢500?
This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 100.
From b), when X = 500, Z = 0.94 has a pvalue of 0.8264
From a), when X = 100, Z = -1.56 has a pvalue of 0.0594
0.8264 - 0.0594 = 0.767
76.7% of customers maintains account balance between GH¢100 and GH¢500
if y=5x what happens to the value of y if the value of x doubles
Answer:
[tex] y = 5x[/tex]
And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:
[tex] y_f = 5(2x) = 10x[/tex]
And if we find the ratio between the two equations we got:
[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]
So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2
Step-by-step explanation:
For this case we have this equation given:
[tex] y = 5x[/tex]
And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:
[tex] y_f = 5(2x) = 10x[/tex]
And if we find the ratio between the two equations we got:
[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]
So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2
18$ for 24 ounces. rate or ratio and in simplest form
Answer:
$3/4 ounces
.75 per ounce
Step-by-step explanation:
Take the dollar amount and divide by the number of ounces
18/24
$3/4 ounces
.75 per ounce
Solve X squared minus 8X +3 equals zero by completing the square which equation is used in the process?
Answer:
x = 4 ± √13
Step-by-step explanation:
x² − 8x + 3 = 0
Complete the square. (-8/2)² = 16.
x² − 8x + 16 − 13 = 0
(x − 4)² − 13 = 0
(x − 4)² = 13
x − 4 = ±√13
x = 4 ± √13
Scores on the Wechsler Adult Intelligence Scale (WAIS) are approximately Normal with mean 105 and standard deviation 16. People with WAIS scores below 73 are considered intellectually disabled when, for example, applying for Social Security disability benefits. According to the 68-95-99.7 rule, about what percent of adults are intellectually disabled by this criterion
Answer:
2.5% of adults are intellectually disabled by this criterion
Step-by-step explanation:
The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 105
Standard deviation = 16
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
What percent of adults are intellectually disabled by this criterion
Below 73
73 = 105 - 2*16
So 73 is 2 standard deviations below the mean.
Of the 50% of the measures that are below the mean, 95% are within 2 standard deviations of the mean, that is, between 73 and 105. The other 100 - 95% = 5% are below 73. So
0.05*0.5 = 0.025
0.025*100 = 2.5%
2.5% of adults are intellectually disabled by this criterion
In a random sample of high school seniors, the proportion who use text messaging was 0.88. In a random sample of high school freshmen, this proportion was 0.68. Researchers found the difference in proportions to be statistically significant and obtained one of the following numbers for the p-value. Which is it?
a. 1.5
b. 0.02
c. 0.78
d. 0.30
Answer:
b. 0.02
Step-by-step explanation:
The smaller the p-value, the stronger the evidence that you should reject the null hypothesis. In this case, this will mean rejecting that the proportions are not significantly different.
Usually, a p-value is considered to be statistically significant when p ≤ 0.05.
From the answer options provided, alternative b. 0.02 is the only one that represents the difference in proportions to be statistically significant (there is only a 2% chance that the proportions are not significantly different).
Therefore, the answer is b. 0.02
if the domain of the square root function f(x) is X greater than or equal to seven which statement must be true 870 subtracted from the exterminator and the radical be the radical was notified by negative number seven turn in Dee the exterminator and the radical has a negative coefficient
[tex]the \: right \: answer \: is \: of \: option \: d \\ please \: see \: the \: attached \: picture \\ hope \: it \: helps[/tex]
Nam owns a used car lot. He checked the odometers of the cars and recorded how far they had driven. He
then created both a histogram and a box plot to display this same data (both diagrams are shown below).
Which display can be used to find how many vehicles had driven more than 200,000 km (kilometers)?
Choose 1 answer:
Answer:
a histogram
Step-by-step explanation:
You can count easily from hiistogram how many vehicles had driven more than 200,000 km (kilometers) and that's not the case with the box plot
a) Write down the inequality for x that is shown on this line.
X
(2)
-5
-3
-2
0
1
3
4 5
N
2 < y < 6 where y is an integer.
b) Write down all the possible values of y.
(2)
c) Solve 3x + 7 2 x + 19
(3)
Total marks: 7
Answer:
a. x<3
b. 3,4,5,6
c.x>6
if you’re good with permutations in math 30 help out with this easy question
In how many ways can five boys and three girls sit in a row such that all boys sit together?
a) 4800
b) 5760
c) 2880
d) 1440
Answer:
2880
Step-by-step explanation:
Consider the 5 boys to be 1 group. The boys and 3 girls can be arranged in 4! ways.
Within the group, the boys can be arranged 5! ways.
The total number of permutations is therefore:
4! × 5! = 2880
What is the length of the diagonal of the square shown below?
Answer:
It’s E
Step-by-step explanation:
The length of the diagonal of the figure considered is given by: Option E: 5√2
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Consider the figure attached below.
The triangle ABC is a right angled triangle as one of its angle is of 90 degrees.
Thus, we can use Pythagoras theorem here to find the length of the diagonal line AC.
Since it is given that:
|AB| = 5 units = |BC|, thus, we get:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|AC| = \sqrt{5^2 + 5^2} = \sqrt{2 \times 5^2} = \sqrt{5^2} \times \sqrt{2} = 5\sqrt{2} \: \rm units[/tex]
We didn't took negative of root as length cannot be negative.
Thus, the length of the diagonal of the figure considered is given by: Option E: 5√2
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
?????????????? Help me
Answer:
Step-by-step explanation:
When we use the distributive property for expanding polynomial products, we often use it in the form ...
(a +b)c = ac +bc
Here, we have ...
(a +b) = (x -1) ⇒ a=x, b=-1
c = (4x+2)
So, the proper application of the distributive property looks like ...
(a +b)c = ac +bc
(x -1)(4x +2) = x(4x+2) -1(4x+2) . . . . . different from the work shown
We must conclude ...
The distributive property was not applied correctly in the first step.
If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?
There are two complex roots.
There are two real roots.
There is one real root.
There is one complex root.
Answer:
There are two complex roots.
Step-by-step explanation:
When the discriminant is a negative number, the parabola will not intersect the x-axis. This means that there are no solutions/two complex solutions.
Please answer this correctly
Answer:
Stem | Leaf
13 | 4 9 9
16 | 0 2 3 6
Step-by-step explanation:
134, 139, 139
160, 162, 163, 166
Determine the quadrant in which the terminal side of the given angle lies.
115°
A. I
B. II
C. III
D. IV
Answer:
[tex] \frac{x}{115}= \frac{2\pi}{360}[/tex]
And solving for x we got:
[tex] x= \frac{115}{160} 2\pi = \frac{23}{36}pi= 0.639 \pi[/tex]
since the value obtained is higher than [tex]\pi/2[/tex] and lower than [tex] \pi[/tex] we can conclude that this angle would be in the second quadrant.
B. II
Step-by-step explanation:
In order to solve this problem we can write the angle in terms of pi using the following proportion rule:
[tex] \frac{x}{115}= \frac{2\pi}{360}[/tex]
And solving for x we got:
[tex] x= \frac{115}{160} 2\pi = \frac{23}{36}pi= 0.639 \pi[/tex]
since the value obtained is higher than [tex]\pi/2[/tex] and lower than [tex] \pi[/tex] we can conclude that this angle would be in the second quadrant.
B. II
Any help would be geeat
Answer:
90 feet
Step-by-step explanation:
==>Given:
Rectangular room measuring 21 feet by 23 feet
==>Required:
Perimeter of the room = the length of all sides of the room
==>Solution:
Using the formula P = 2L + 2W, we can find the perimeter of the rectangular room assuming that length big the room (L) = 23 ft, while the width (W) = 22 ft.
Therefore,
P = 2(23) + 2(22)
P = 46 + 44
P = 90 ft
Perimeter of the room = 90 feet
please hurry I’ll make brainiest
A marble is thrown off of a balcony, towards the ground, from a height
of 18 feet above ground level, with a velocity of 4.5 feet per second.
Which function could be used to model the height of the marble, after
t seconds?
Answer:
Option (3)
Step-by-step explanation:
A stone has been thrown off towards the ground from a height [tex]h_{0}[/tex] = 18 feet
Initial speed of the stone 'u' = 4.5 feet per second
Since height 'h' of a projectile at any moment 't' will be represented by the function,
h(t) = ut - [tex]\frac{1}{2}(g)(t)^2[/tex] + [tex]h_{0}[/tex]
h(t) = 4.5t - [tex]\frac{1}{2}(32)t^2[/tex]+ 18 [ g = 32 feet per second square]
h(t) = 4.5t - 16t² + 18
h(t) =-16t² + 4.5t + 18
Therefore, Option (3) will be the answer.
The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages ( x ) in the city has the following probability distribution.xf (x)00.8010.1520.0430.01The mean and the standard deviation for the number of electrical outages (respectively) are _____.
Answer:
Therefore, the mean and the standard deviation for the number of electrical outages (respectively) are 0.26 and 0.5765 respectively.
Step-by-step explanation:
Given the probability distribution table below:
[tex]\left|\begin{array}{c|cccc}x&0&1&2&3\\P(x)&0.8&0.15&0.04&0.01\end{array}\right|[/tex]
(a)Mean
Expected Value, [tex]\mu =\sum x_iP(x_i)[/tex]
=(0*0.8)+(1*0.15)+(2*0.04)+(3*0.01)
=0+0.15+0.08+0.03
Mean=0.26
(b)Standard Deviation
[tex](x-\mu)^2\\(0-0.26)^2=0.0676\\(1-0.26)^2=0.5476\\(2-0.26)^2=3.0276\\(3-0.26)^2=7.5076[/tex]
Standard Deviation [tex]=\sqrt{\sum (x-\mu)^2P(x)}[/tex]
[tex]=\sqrt{0.0676*0.8+0.5476*0.15+3.0276*0.04+7.5076*0.01}\\=\sqrt{0.3324}\\=0.5765[/tex]
Therefore, the mean and the standard deviation for the number of electrical outages (respectively) are 0.26 and 0.5765 respectively.
(4a - 3b + 4c) + (8a - 2b + 3c)
Answer:
Hey mate, here's ur answer:
----------------------------------------------------------
(4a - 3b + 4c) + (8a - 2b + 3c)
=4a+−3b+4c+8a+−2b+3c
=(4a+8a)+(−3b+−2b)+(4c+3c)
=12a−5b+7c
----------------------------------------------------------
Hope it helps
#stayhomestaysafemate
:D
Complete the paragraph proof. Given: and are right angles Line segment A B is-congruent-to line segment B C Line segment B C is-congruent-to line segment A C Prove: Line A R bisects Angle B A C Triangles A B R and R C A share side R A. A line is drawn from point B to point C and intersects side A R at point P. It is given that and are right angles, and . Since they contain right angles, ΔABR and ΔACR are right triangles. The right triangles share hypotenuse , and reflexive property justifies that . Since and , the transitive property justifies . Now, the hypotenuse and leg of right ΔABR is congruent to the hypotenuse and the leg of right ΔACR, so by the HL congruence postulate. Therefore, ________ by CPCTC, and bisects by the definition of bisector.
Answer:
<BAR ≅<CAR
Step-by-step explanation:
Just took the test
Answer:
A edg 2020
Step-by-step explanation:
SELECT THE EQUIVALENT EXPRESSION
(6^-4 x 8^-7)^-9
A. 6^36•8^63
B. 1/6^13•8^16
Answer:
A
Step-by-step explanation:
Calculate the products in the multiple choice and see if any equal the product in the problem.
Hence as the products calculated in choice A equal that in the problem;the answer is A
If (-2, y) lies on the graph of y=3x, then y=
1/9
0-6
hi
if reduce equation of line is y = 3x
and if x = -2 so y = 3*-2 = -6
Suppose GRE Quantitative scores are normally distributed with a mean of 587587 and a standard deviation of 152152. A university plans to offer tutoring jobs to students whose scores are in the top 14%14%. What is the minimum score required for the job offer? Round your answer to the nearest whole number, if necessary.
Answer:
The minimum score required for the job offer is 751.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 587, \sigma = 152[/tex]
What is the minimum score required for the job offer?
Top 14%, so the minimum score is the 100-14 = 86th percentile, which is X when Z has a pvalue of 0.86. So X when Z = 1.08.
Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.08 = \frac{X - 587}{152}[/tex]
[tex]X - 587 = 1.08*152[/tex]
[tex]X = 751.16[/tex]
Rounding to the nearest whole number:
The minimum score required for the job offer is 751.
(Geometry) PLZ HELP ASAP
Answer:
121 square feet
Step-by-step explanation:
The area of a triangle is the height multiplied by the base divided by 2. Since this is a right triangle, you can simply use the two legs for this. The area of this triangle is therefore:
[tex]\dfrac{24.2\cdot 10}{2}=\dfrac{242}{2}=121[/tex]
Hope this helps!
Answer:
Area: 121 feet²
Step-by-step explanation:
The formula for the area of any triangle is [tex]\frac{1}{2} *b*h[/tex]
This triangle's base is 10 feet
This triangle's height is 24.2 feet
[tex]\frac{1}{2} *10*24.2=\\5*24.2=\\121[/tex]
The area of the triangle is 121 square feet or 121 ft²
What is the final amount if 784 is decreased by 1% followed by a 4% increase?
Give your answer rounded to 2 DP.
Answer:
3136
Step-by-step explanation:
Thats the answer please I don't have time to write the explanation
The volume of a sphere is approximately 1767.1459 cubic inches. What is the length of the radius of the sphere the nearest tenth?
Answer:
7.5 in
Step-by-step explanation:
Step one
This problem bothers on the mensuration of solid shapes, a sphere.
We know that the volume of a sphere is expresses as
V= (4/3) πr³
Given that the volume of the sphere is
1767.1459 in³
To solve for the radius r we need to substitute the value of the volume in the expression for the volume we have
Step two
1767.1459= (4/3) πr³
1767.1459*3= 4πr³
5301.4377/4*3.142=r³
421.82031=r³
Step three
To get r we need to cube both sides we have
r= ³√421.82031
r= 7.49967589711
To the nearest tenth
r= 7.5 in
If a triangle has sides that are 21 and 6 what is the range for third side x?
Enter your answer without spaces in range format.
Example: 1<x<3
Answer:
15<x<27
Step-by-step explanation:
Rule for the sides of a triangle:
The sum of the two smallest sides of a triangle must be greater than the biggest side.
In this question:
Sides of 6, 21 and x. We have to find the range for x.
If 21 is the largest side:
Two smallest are 6 and x.
x + 6 > 21
x > 21 - 6
x > 15
If x is the largest side:
Two smallest and 6 and 21. So
21 + 6 > x
27 > x
x < 27
Then
x has to be greater than 15 and smaller than 27. So the answer is:
15<x<27
If M ⊥ N and L ∥ M, then _____
Answer:
L ⊥ N
Step-by-step explanation:
Since M and N are perpendicular, and L is parallel to M, anything that's perpendicular to M is also perpendicular to L. In fact, since we have parallel lines, we now have many sets of congruent angles, but the only ones we know the actual measurements of are the right angles from the perpendicular lines.