Answer:
Step-by-step explanation:
2 3x6
the 3 is an exponet so supost to be smaller
the answer- 2^3 x^6
i think its right
What’s the correct answer for this?
Answer:
A:
Step-by-step explanation:
Using tangent-secant theorem
AE²=(EC)(ED)
12²=(8)(8+x+10)
144=8(x+18)
144=8x+144
8x = 144-144
8x = 0
So
x = 0
Now
ED = 8+x+10
ED = 8+0+10
ED = 18
please help me on this work please !
A stone is thrown vertically into the air at an initial velocity of 79 ft/s. On a different planet, the height s (in feet) of the stone above the ground after t seconds is sequals79tminus3t squared and on Earth it is sequals79tminus16t squared. How much higher will the stone travel on the other planet than on Earth?
Answer:
[tex]13t^2[/tex] feet higher the stone will travel on the other plant than on Earth.
Step-by-step explanation:
Initial velocity of the stone thrown vertically = 79 ft/s
It is given that:
Height attained on a different planet with time [tex]t[/tex]:
[tex]s_p = 79t -3t^2[/tex]
Height attained on Earth with time [tex]t[/tex]:
[tex]s_e = 79t -16t^2[/tex]
If we have a look at the values of [tex]s_p\text{ and }s_e[/tex], it can be clearly seen that the part [tex]79t[/tex] is common in both of them and some values are subtracted from it.
The values subtracted are [tex]3t^2\text{ and } 16t^2[/tex] respectively.
[tex]t^2[/tex] can never be negative because it is time value.
So, coefficient of [tex]t^2[/tex] will decide which is larger value that is subtracted from the common part i.e. [tex]79t[/tex].
Clearly, [tex]3t^2\text{ and } 16t^2[/tex] have [tex]16t^2[/tex] are the larger value, hence [tex]s_e < s_p[/tex].
So, difference between the height obtained:
[tex]s_p - s_e = 79t - 3t^2 - (79t - 16t^2)\\\Rightarrow 79t -3t^2 - 79t + 16t^2\\\Rightarrow 13t^2[/tex]
So, [tex]13t^2[/tex] feet higher the stone will travel on the other plant than on Earth.
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[tex]1. \: (x - y) {2} \\ = {x}^{2} - 2xy + {y}^{2} \\ 2. \: (a + b) ^{2} \\ = {a}^{2} + 2ab + {b}^{2} \\ 3. \: (2x + 3y) ^{2} \\ = {(2x)}^{2} + 2.2x.3y + (3y) ^{2} \\ = {4x}^{2} + 12xy + {9y}^{2} \\ 4.(3x - 2y) ^{2} \\ = (3x) ^{2} - 2.3x.2y + (2y) ^{2} \\ = {9x}^{2} - 12xy + {4y}^{2} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
a) x^2−2xy+y^2
b) a^2 -ab+b^2
c)4x^2+12xy+9y^2
d)9x^2 -12xy+4y^2
Step-by-step explanation:
a) x^2−2xy+y^2
b) a^2 -ab+b^2
c)4x^2+12xy+9y^2
d)9x^2 -12xy+4y^2
We rewrite (x-y)^2 as (x-y) (x-y) to show and always see + sign at start for question a ) and question b)
a) x*x+x(−y)−yx−y(−y) = x^2−2xy+y^2
b) a^2 becomes a^2 -ab as a^2 -ab+b^2
c) As shown in notes attached and this will help you most.
d) the reasons we keep +4y is because -2y becomes -2y-2y and creates a plus.
Complete the point- slope equation of the line through (8, -8 and (9, 8). Y - 8 =
When writing expressions for complex numbers, what does i represent?
Answer:
see below
Step-by-step explanation:
i is the imaginary number and it represents the square root of -1
Find the exact length of the third side. (Pythagorean Theorem)
Answer:
3 sqrt(5) =c
Step-by-step explanation:
We can use the pythagorean theorem
a^2 + b^2 = c^2
3^2 + 6^2 = c^2
9+36 = c^2
45 = c^2
Take the square root of each side
sqrt(45) = sqrt(c^2)
sqrt(9)sqrt(5) = c
3 sqrt(5) =c
What is the value of d21+d22+d23 given the matrix equation below?
Answer:
B. 8
Step-by-step explanation:
The question lacks the required diagram. Find the diagram in the attachment.
Before we can find d21, d22 and d23, we need to get the matrix D first as shown in the attached solution.
On comparison as shown in the attachment, d21 = 11, d22 = -10 and d23 = 7
Note that d21 refers to element in the second row and first column of the matrix
d22 is the element in the second row and second column of the matrix
d23 is the element in the second row and third column of the matrix
d21+d22+d23 = 11-10+7
d21+d22+d23 = 8
The second option is correct.
Express the following ratio in its simplest form.
4:12
Answer:
3:12
Step-by-step explanation:
Answer:
1:3
Step-by-step explanation:
Think 4:12 as a fraction for a moment, it would be 4/12. Now completely simplify 4/12, you get 1/3. Now put 1/3 as a ratio, it would be 1:3.
Please mark BRAINLIEST, thanks!
Do all perpendicular lines have negative reciprocal slopes?
Not necessarily, the more correct definition is opposite reciprocal slopes.
The example used is how horizontal and vertical lines are parallel. Horizontal lines have a slope of 0, also written as 0/1. However, vertical lines have an undefined slope, which isn't necessarily negative. It has a slope of 1/0, which is undefined. In this case, the reciprocal isn't negative.
In all other cases (1 and -1, 2 and -1/2, etc.) yes, the perpendicular pairs are negative and reciprocal.
find the quotient of 25.5÷0.5
Answer:
[tex]51[/tex]
Step-by-step explanation:
[tex]\frac{25.5}{0.5}[/tex]
[tex]\frac{255}{5}[/tex]
[tex]=51[/tex]
Steve wants to use his 18% employee discount to buy a video game that has a regular price of $69.99. A 6.5% sales tax is applied to the discounted price. How much will he pay for the game, including sales tax?
Answer:
$61.12
Step-by-step explanation:
Price of the Video game = $69.99
Discount = 18%
Discount price = 18% of $69.99
= $69.99*18/100
= $12.6
Price after Discount = Price - Discount price
= $69.99 - $12.6
= $57.39
Sales tax = 6.5% applied to the discounted price
= 6.5% of $57.39
sales tax in dollars = $57.39 * 6.5/100
= $3.73
The amount he pays for the game = $57.39 + $3.73
= $61.12
A researcher classifies firefighters according to whether their gloves fit well or poorly and by gender. They want to know if there is a difference in the proportion of poorly fitted gloves and gender. At alpha = 0.01, use the chi-square test to determine if there is a difference in the population proportion of glove fitness for the two genders.
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly
Gloves fit well
Total
Answer:
Step-by-step explanation:
Hello!
The objective is to test if the proportion of "X: gloves fitness, categorized: Fit poorly and Fit well" is the same for two populations of interest, "male firefighters" and "female firefighters"
To do this you have to conduct a Chi-Square test of Homogeneity.
In the null hypothesis you have to state that the proportion of the categories of the variable are the same for all the populations of interest.
Be
M: the firefighter is male
F: the firefighter is female
Y: represents the category that the gloves "fit poorly"
W: represents the category that the gloves "fit well"
The null hypothesis will be:
H₀: P(Y|M)=P(Y|F)=P(Y)
P(W|M)=P(W|F)=P(W)
H₁: At least one of the statements in the null hypothesis is false.
α: 0.01
To calculate the statistic under the null hypothesis you have to calculate the expected frequencies first:
[tex]E_{ij}= O_{.j}*\frac{O_{i.}}{n}[/tex]
O.j= total of the j-column
Oi.= total of the i-row
n= total of observations
[tex]E_{11}= 547*\frac{152}{586} = 141.88[/tex]
[tex]E_{12}=39*\frac{152}{586}= 10.12[/tex]
[tex]E_{21}= 547*\frac{434}{586} = 405.12[/tex]
[tex]E_{22}= 39*\frac{434}{586} = 28.88[/tex]
[tex]X^2= sum \frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~~~X^2_{(r-1)(c-1)}[/tex]
r= number of rows (in this case 2)
c=number of columns (in this case 2)
[tex]X^2_{H_0}= \frac{(132-141.88)^2}{141.88} +\frac{(20-10.12)^2}{10.12} +\frac{(415-405.12)^2}{405.12} +\frac{(19-28.88)^2}{28.88} = 13.95[/tex]
Using the critical value approach, you have to remember that this test is always one-tailed to the right, meaning that you'll have only one critical value from which the rejection region is defined:
[tex]X^2_{(r-1)(c-1);1-\alpha }= X^2_{1;0.99}= 6.635[/tex]
The decision rule is then:
If [tex]X^2_{H_0}[/tex] ≥ 6.635, reject the null hypothesis.
If [tex]X^2_{H_0}[/tex] < 6.635, do not reject the null hypothesis.
The calculated value is greater than the critical value, the decision is to reject the null hypothesis.
So at a 1% level you can conclude that this test is significant. This means that the proportions of gloves fitness, categorized in "Fit poorly" and "Fit well" are different for the male and female firefighters populations.
I hope this helps!
Answer:
The Chi - Square Test Statistics is 13.98
p-value = 0.0002
CONCLUSION: Since the p-value is less than the level of significance ; (i.e p-value < ∝) we reject the null hypothesis and accept the alternative hypothesis.
Thus; there is a difference in the population proportion of glove fitness for the two genders.
Step-by-step explanation:
From the information given ; the structure of the table can be well represented as follows;
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly
Gloves fit well
Total
The objective of this question is to use the chi-square test to determine if there is a difference in the population proportion of glove fitness for the two genders.
We call represent the hypothesis as follows:
The null hypothesis: [tex]H_o:[/tex] states that there is no difference in the population proportion of glove fitness for the two genders.
The alternative hypothesis: [tex]H_a[/tex] states that there is difference in the population proportion of glove fitness for the two genders.
The expected frequency of a particular cell can be calculated by multiplying the sum of the rows and columns together, then dividing it by the Total sum
For row 1 column 1 (gloves fit poorly (male) ; we have:
[tex]= \dfrac{547*152}{586} =141.884\\[/tex]
For row 2 column 1 (gloves fit well(male) ; we have:
[tex]= \dfrac{547*434}{586} =405.116[/tex]
For row 1 column 2 (gloves fit poorly (female)) ; we have:
[tex]= \dfrac{39*152}{586} =10.116[/tex]
For row 2 column 2 ( gloves fit well ( female ) ; we have:
[tex]= \dfrac{39*434}{586} =28.884[/tex]
Thus; we can have the complete table to now be:
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly 141.884 10.116 152
Gloves fit well 405.116 28.884 434
Total 547 39 586
The Chi - Square Test Statistics can be calculated via the formula:
[tex]X^2 = \dfrac{\sum (f_o-f_e)^2}{f_e}[/tex]
where;
[tex]f_o[/tex] = observed data frequency
[tex]f_e[/tex] = expected data frequency
∴
The Chi - Square Test Statistics is as follows:
[tex]=\dfrac{(131-141.884)^2}{141.884} + \dfrac{(20-10.116)^2}{10.116}+ \dfrac{(415-405.116)^2}{405.116}+ \dfrac{(39-28.884)^2}{28.884}[/tex]
= 0.68+9.6+0.2+3.5
= 13.98
We are given the level of significance ∝ to be = 0.01
numbers of rows = 2; number of column = 2
Thus; the degree of freedom = (2-1)(2-1) = 1×1 = 1
Using the Excel Function : [ = CHISQ.DIST.RT²(X²,df)]
p-value = 0.0002
CONCLUSION: Since the p-value is less than the level of significance ; (i.e p-value < ∝) we reject the null hypothesis and accept the alternative hypothesis.
Thus; there is a difference in the population proportion of glove fitness for the two genders.
g Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 6 ft high
Answer:
0.3537 feet per minute.
Step-by-step explanation:
Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.
[tex]\dfrac{dV}{dt}=10$ ft^3/min[/tex]
[tex]\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h[/tex]
If the Base Diameter = Height of the Cone
The radius of the Cone = h/2
Therefore,
[tex]\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}[/tex]
[tex]\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}[/tex]
Therefore: [tex]\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10[/tex]
We want to determine how fast is the height of the pile is increasing when the pile is 6 feet high.
[tex]When h=6$ feet$\\\dfrac{3\pi *6^2}{12}\dfrac{dh}{dt}=10\\9\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{9\pi}\\ \dfrac{dh}{dt}=0.3537$ feet per minute[/tex]
When the pile is 6 feet high, the height of the pile is increasing at a rate of 0.3537 feet per minute.
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?
Answer:
When x is 2, y is 16
Step-by-step explanation:
If y is 48 and x is 6, then y is 8 when x is 1.
Because of this, when x is 2, y will be 16.
Please mark Brainliest
The perimeter of the rectangle is below 76 units. Find the length of side AD. AB on rectangle 3y + 3 CB 2y
Answer:
14 units
Step-by-step explanation:
The perimeter of a figure is the sum of the lengths of all the sides.
Here, we know that ABCD is a rectangle, so by definition, AB = CD and AD = BC. We also are given that AB = 3y + 3 and BC = 2y, which means that:
AB = CD = 3y + 3
AD = BC = 2y
Adding up all the side lengths and setting that equal to the perimeter, which is 76 units, we get the expression:
AB + CD + AD + BC = 76
(3y + 3) + (3y + 3) + 2y + 2y = 76
10y + 6 = 76
10y = 70
y = 7
We want to know the length of AD, which is written as 2y. Substitute 7 in for y:
AD = 2y = 2 * 7 = 14
The answer is thus 14 units.
~ an aesthetics lover
Answer:
14
Step-by-step explanation:
The perimeter of a rectangle is found by
P = 2 (l+w)
P = 2( 3y+3+2y)
Combine like terms
P = 2(5y+3)
We know the perimeter is 76
76 = 2(5y+3)
Divide each side by 2
76/2 = 2/2(5y+3)
38 = 5y+3
Subtract 3 from each side
38-3 = 5y+3-3
35 = 5y
Divide each side by 5
35/5 = 5y/5
7 =y
We want the length of AD = BC = 2y
AD = 2y=2*y = 14
Suppose that a researcher is planning a new study on hemoglobin levels amongst women under 25 years old. Previous research suggest that the standard deviation of hemoglobin is 0.7 g/dl. In the new study the research wants to have the standard error for the sample mean to be no more than 0.05 g/dl. Find the required sample size for the new study.
Answer:
A sample size of at least 531 is required.
Step-by-step explanation:
We are lacking the confidence level to solve this question, so i am going to use a 90% confidence level.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Find the required sample size for the new study.
A sample size of at least n is required.
n is found when [tex]M = 0.05[/tex]
We have that [tex]\sigma = 0.7[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.05 = 1.645*\frac{0.7}{\sqrt{n}}[/tex]
[tex]0.05\sqrt{n} = 1.645*0.7[/tex]
[tex]\sqrt{n} = \frac{1.645*0.7}{0.05}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.645*0.7}{0.05})^{2}[/tex]
[tex]n = 530.4[/tex]
Rounding up
A sample size of at least 531 is required.
01:30:4
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the
solution set of this problem?
Answer:
x<_ 21
Step-by-step explanation:
5(x+27)>_ =6(x+26)
5x +135 >_ 6x +156
5x >_6x +21
-x>_21
x<_21
no guess please explain
Find the diameter and radius of a circle with a circumference of 65.98 Please help
Answer:
21 and 10.5 respectively
Step-by-step explanation:
Remember circumference of a circle is given as;
C= 2×π×r; r is raduis
r = C / 2×π
=65.98/(2×3.142)= 10.50
D= 2× r = 2× 10.50= 21.0( D represent diameter)
Note π = 3.142 a known constant
i have a problem on statistics
5. Data on household vehicle miles of travel (VMT) are compiled annually by the Federal Highway Administration and are published in National Household Travel Survey, Summary of Travel Trends. Independent random samples of 15 midwestern households and 14 southern households provided the following data on last year’s VMT, in thousands of miles. At the 5% significance level, does there appear to be a difference in last year’s mean VMT for midwestern and southern households? Use both p-value and critical value approach. Assume population variance to be equal
Midwest
16.2 , 14.6 , 11.2 , 24.4 , 9.4 12.9 , 18.6 , 16.6 , 20.3 ,15.1 , 17.3 , 10.8 , 16.6 , 20.9 , 18.3
South
22.2, 19.2 , 9.3 , 24.6 ,20.2 , 15.8, 18.0 , 12.2 , 20.1 , 16.0 , 17.5 , 18.2 , 22.8 , 11.5
Answer:
Step-by-step explanation:
Hello!
The objective is to compare the VMT of mid western households and southwestern households. For this two independent random samples of households from both areas and their VMT were recorded:
Be
X₁: VMT of a mid western household
Midwest
16.2 , 14.6 , 11.2 , 24.4 , 9.4 12.9 , 18.6 , 16.6 , 20.3 ,15.1 , 17.3 , 10.8 , 16.6 , 20.9 , 18.3
n₁= 15
∑X₁= 243.20
∑X₁²= 4175.98
X[bar]₁= 16.21
S₁²= 16.64
S₁= 4.08
X₂: VMT of a southwestern household
22.2, 19.2 , 9.3 , 24.6 ,20.2 , 15.8, 18.0 , 12.2 , 20.1 , 16.0 , 17.5 , 18.2 , 22.8 , 11.5
n₂= 14
∑X₂= 247.60
∑X₂²= 4633.24
X[bar]₂= 17.69
S₂²= 19.56
S₂= 4.42
The parameters of study are the population means, if the claim is that the VMT of households is different in both areas, then you'd expect the population means to be different too.
The hypotheses are:
H₀: μ₁ = μ₂
H₁: μ₁ ≠ μ₂
α: 0.05
Assuming both populations are normal and since both population variances are equal the test to apply is an independent samples t test pooled variance:
[tex]t= \frac{(X[bar]_1-X[bar]2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]
[tex]Sa^2= \frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} = \frac{14*16.67+13*19.56}{15+14-2}= \frac{487.66}{27} = 18.06[/tex]
Sa= 4.249= 4.25
[tex]t_{H_0}= \frac{(16.21-17.69)-0}{4.25*\sqrt{\frac{1}{15} +\frac{1}{14} } }= -0.937= -0.94[/tex]
Critical value approach:
This test is two-tailed, this means that the rejection region is divided in two tails:
[tex]t_{n_1+n_2-2; \alpha /2}= t_{27; 0.025}= -2.052[/tex]
[tex]t_{n_1+n_2-2; 1-\alpha /2}= t_{27; 0.975}= 2.052[/tex]
The decision rule is:
If [tex]t_{H_0}[/tex] ≤ -2.052 or if [tex]t_{H_0}[/tex] ≥ 2.052, reject the null hypothesis.
If -2.052 < [tex]t_{H_0}[/tex] < 2.052, do not reject the null hypothesis.
The calculated value is within the "no rejection region" so the decision is to not reject the null hypothesis.
Using the p-value approach:
The p-value is the probability of obtaining a value as extreme as the calculated value of the statistic under the null hypothesis ([tex]t_{H_0}[/tex]). Just as the significance level, the p-value is two tailed, you can calculate it as:
P(t₂₇ ≤ -0.93) + P(t₂₇ ≥ 0.93)= P(t₂₇ ≤ -0.93) + (1 - P(t₂₇ < 0.93)= 0.1796 + ( 1 - 0.8204)= 0.1796*2= 0.3592
p-value= 0.3592
The p-value is always compared to the significance level, the decision rule for this approach is:
If the p-value ≤ α, reject the null hypothesis.
If the p-value > α, do not reject the null hypothesis.
The p-value is greater than α, so the decision is to not reject the null hypothesis.
At a 5% significance level, there is no significant evidence to reject the null hypothesis. You can conclude that the population means of the VMT for households of the Midwest South ers households.
I hope this mhelps!
Evaluate the function h(t) =|t +2| + 3; find h(6)
Answer:
11
Step-by-step explanation:
h(t) =|t +2| + 3
Let t=6
h(6) =|6 +2| + 3
= |8| +3
=8+3
= 11
Solve the equation and state a reason for each step.
23+11a-2c=12-2c
Simplifying
23 + 11a + -2c = 12 + -2c
Add '2c' to each side of the equation.
23 + 11a + -2c + 2c = 12 + -2c + 2c
Combine like terms: -2c + 2c = 0
23 + 11a + 0 = 12 + -2c + 2c
23 + 11a = 12 + -2c + 2c
Combine like terms: -2c + 2c = 0
23 + 11a = 12 + 0
23 + 11a = 12
Solving
23 + 11a = 12
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-23' to each side of the equation.
23 + -23 + 11a = 12 + -23
Combine like terms: 23 + -23 = 0
0 + 11a = 12 + -23
11a = 12 + -23
Combine like terms: 12 + -23 = -11
11a = -11
Divide each side by '11'.
a = -1
Simplifying
a = -1
average of a data set was 40, and that standard deviation was 10, what else could you derive from that information.
Answer:
[tex] \bar x = 40, s =10[/tex]
And from these values we can estimate the sample variance like this:
[tex] s^2 = 10^2 =100[/tex]
And we can also estimate the coeffcient of variation given by:
[tex] \hat{CV} =\frac{s}{\bar x}[/tex]
And replacing we got:
[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]
And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.
Step-by-step explanation:
For this case we have the following info given:
[tex] \bar x = 40, s =10[/tex]
And from these values we can estimate the sample variance like this:
[tex] s^2 = 10^2 =100[/tex]
And we can also estimate the coeffcient of variation given by:
[tex] \hat{CV} =\frac{s}{\bar x}[/tex]
And replacing we got:
[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]
And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.
You have already a 1000 cash on your hand. You have also a 1000 cash in bank and you withdraw half of 500, so, it means you withdraw 250. Now, you have a 1000 cash on hand plus 250 that you have been withdraw from the bank, all in all you have 1250 now in your hand.
Answer: At the end, you have $750 remaining in the bank.
Step-by-step explanation:
I guess you want to know how much is left in the bank.
initially
Hand : $1000
Bank: $1000
you withdraw $250 from the bank:
Hand: $1000 + $250 = $1250
Bank: $1000 - $250 = $750
There are 225 students at March middle school. On Friday, 135 students wore spirit shirts. What percent of the students did Not wear spirit shirts on Friday?
Answer:
40%
Step-by-step explanation:
To find the answer to this, you first can find out what percentage of students did wear spirit shirts. To do this you can divide 135 by 225 to give you 0.6. To convert the decimal into a percentage you can simply multiply by 100, giving you 60%. Then to find the percentage of students that did not wear spirit shirts, you can subtract 60 from 100, giving you 40%.
Ronnie invested $1500 in an account that earns 3.5% interest, compounded annually. The formula for compound interest is A(t) = P{(1 + i)^t}A(t)=P(1+i) t . How much did Ronnie have in the account after 4 years?
Answer:
BStep-by-step explanation:
A= New amount
P= Principal or Original amount which is £1500
I= Interest
t= time period
3.5% as a decimal is 3.5÷100=0.035
time period= 4 years
so 1500(1+0.035)^4 = B
What’s the correct answer for this question?
Answer:
D
Step-by-step explanation:
It would be a cone with a radius of 4 units rotating around y-axis.
A university warehouse has received a shipment of 25 printers, of which 10 are laser printers and 15 are inkjet models. If 6 of these 25 are selected at random to be checked by a particular technician, what is the probability that exactly 3 of those selected are laser printers (so that the other 3 are inkjets)
Answer:
The probability is 0.31
Step-by-step explanation:
To find the probability, we will consider the following approach. Given a particular outcome, and considering that each outcome is equally likely, we can calculate the probability by simply counting the number of ways we get the desired outcome and divide it by the total number of outcomes.
In this case, the event of interest is choosing 3 laser printers and 3 inkjets. At first, we have a total of 25 printers and we will be choosing 6 printers at random. The total number of ways in which we can choose 6 elements out of 25 is [tex]\binom{25}{6}[/tex], where [tex]\binom{n}{k} = \frac{n!}{(n-k)!k!}[/tex]. We have that [tex]\binom{25}{6} = 177100[/tex]
Now, we will calculate the number of ways to which we obtain the desired event. We will be choosing 3 laser printers and 3 inkjets. So the total number of ways this can happen is the multiplication of the number of ways we can choose 3 printers out of 10 (for the laser printers) times the number of ways of choosing 3 printers out of 15 (for the inkjets). So, in this case, the event can be obtained in [tex]\binom{10}{3}\cdot \binom{15}{3} = 54600[/tex]
So the probability of having 3 laser printers and 3 inkjets is given by
[tex] \frac{54600}{177100} = \frac{78}{253} = 0.31[/tex]
In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf)
Here is the full question.
The average finishing time among all high school boys in a particular track event in a certain state is 5 minutes 17 seconds. Times are normally distributed with standard deviation 12 seconds.
A. The qualifying time in this event for participation in the state meet is to be set so that only the fastest 5% of all runners qualify. Find the qualifying time in seconds (round it to the closest second). (Hint: Convert minutes to seconds.)
B. In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf)
Answer:
a. x ≅ 337 seconds.
b. P(x > 337 ) = 0.1056
Step-by-step explanation:
A.
Given that ;
Mean [tex]\mu =[/tex] 5 minutes 17 seconds =( (60× 5)+17 ) seconds = 317 seconds ( since 60 seconds make 1 minute.
Standard deviation: [tex]\sigma[/tex] = 12 seconds.
Only the fastest 5% of all runners qualify
The objective is to determine the qualifying time in seconds
Let's look for the Z-score of 0.95;
The Z-score is 1.645 from the tables
[tex]x= ( \sigma * z ) + \mu[/tex]
[tex]x = ( 12 * 1.645 ) + 317 \\ \\x = 336.74[/tex]
x ≅ 337 seconds.
B. Given that the standard deviation = 12 seconds
Mean = 5 minutes 22 seconds = (5 × 60 + 22 )seconds = 322 seconds
he objective is to find P(x > 337 ) i.e the proportion of boys from this region who qualify to run in this event in the state meet.
we are using command normalcdf (SEE THE ATTACHED FILE BELOW FOR THE COMPUTATION)
we have P(x > 337 ) = 0.1056
