Set up two equations:
Let a = adults and c = child:
a + c = 289 ( rewrite as a = 289 - c)
1.50c + 4a = 746
Replace a with the rewritten formula:
1.50c + 4(289-c) = 746
SImplify:
1.50c + 1156 - 4c = 746
Combine like terms:
-2.50c + 1156 = 746
Subtract 1156 from both sides:
-2.50c = -410
Divide both sides by -2.50
c = -410 / -2.50 = 164
Number of children = 164
Number of adults = 289 - 164 = 125
Answer:
[tex] x+y = 289[/tex] (1) total people entered
[tex] 1.50 x +4 y = 746[/tex] (2) total amount collected
From the first equation we can solve for x and we got:
[tex] x = 289-y[/tex] (3)
Replacing (3) into (2) we got:
[tex] 1.5(289-y) +4y = 746[/tex]
And solving for y we got:
[tex] 433.5 -1.5 y +4y = 746[/tex]
[tex] 2.5 y= 312.5[/tex]
[tex]y=\frac{312.5}{2.5}= 125[/tex]
And then using (3) we can solve for x and we got:
[tex] x= 289-125= 164[/tex]
So then we have:
number of children = 164
number of adults = 125
Step-by-step explanation:
Let x the number of children and y the number of adults. From the info given we can set up the following equations:
[tex] x+y = 289[/tex] (1) total people entered
[tex] 1.50 x +4 y = 746[/tex] (2) total amount collected
From the first equation we can solve for x and we got:
[tex] x = 289-y[/tex] (3)
Replacing (3) into (2) we got:
[tex] 1.5(289-y) +4y = 746[/tex]
And solving for y we got:
[tex] 433.5 -1.5 y +4y = 746[/tex]
[tex] 2.5 y= 312.5[/tex]
[tex]y=\frac{312.5}{2.5}= 125[/tex]
And then using (3) we can solve for x and we got:
[tex] x= 289-125= 164[/tex]
So then we have:
number of children = 164
number of adults = 125
plzz help brainliest thanks and 20 points Look at the cups shown below (images are not drawn to scale): A cone is shown with width 2 inches and height 3 inches, and a cylinder is shown with width 2 inches and height 7 inches. How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth. 18.8 cubic inches 21.9 cubic inches 25.1 cubic inches 32.6 cubic inches
Answer:
18.8 cubic inches
Step-by-step explanation:
1. Solve for the volume of Cup A. (volume of a cone = 1/3πr² · h)
1/3 · 3.14 · 1² · 3 = 3.14 in³
2. Solve for the volume of Cup B (volume of a cylinder = πr² · h)
3.14 · 1² · 7 = 21.98 in³
3. Subtract the volume of Cup A from Cup B
21.98 - 3.14 = 18.84
4. Round 18.84 to the nearest tenth
18.84 → 18.8 in.³
Answer:
18 .8
Step-by-step explanation:
got it right on test
4 1/2 +1 3/5 (in the simplest form)
6 1/10
Step-by-step explanation:
4 + 1/2+1+3/5
5+1+1/10=6 1/10
can i please get help with this
Step-by-step explanation:
Intersecting secant angles theorem: The angle between two secants is half the difference of the intersected arcs.
52 = ½ (x − 38)
x = 142
Arc angles add up to 360.
360 = 80 + 38 + z + x
z = 100
Tangent-chord theorem: The angle between a tangent and a chord is half the intercepted arc angle.
y = x/2
y = 71
Show all work for 135 points (90 points + brainliest = 135 pts)
Answer:
(a) 5/7 chance
(b) 2/7 chance
(c) 5/7 chance
Step-by-step explanation:
Event X: There are 3 letters that come before "D". A, B, and C. There is a 3 out of 7 chance of picking one of those letters. (3/7)
Event Y: There are 4 letters in "C A G E". Those 4 letters are in the 7 first letters of the alphabet meaning that they are in our pile of tiles. There is a 4 out of 7 chance of picking one of those letters. (4/7)
(a) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 5/7 chance of either Event X or Event Y happening since tiles "A" and "C" are included in both events.
(b) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 2/7 chance of both X and Y happening since there are only 2 tiles that are the same in both events, "A" and "C". (We are only allowed to pick one tile)
(c) The complement of Event Y is 1-4/7=5/7 chance.
Answer:
a) 5/7 chance
(b) 2/7 chance
(c) 5/7 chance
Step-by-step explanation:
Event X: There are 3 letters that come before "D". A, B, and C. There is a 3 out of 7 chance of picking one of those letters. (3/7)
Event Y: There are 4 letters in "C A G E". Those 4 letters are in the 7 first letters of the alphabet meaning that they are in our pile of tiles. There is a 4 out of 7 chance of picking one of those letters. (4/7)
(a) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 5/7 chance of either Event X or Event Y happening since tiles "A" and "C" are included in both events.
(b) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 2/7 chance of both X and Y happening since there are only 2 tiles that are the same in both events, "A" and "C". (We are only allowed to pick one tile)
(c) The complement of Event Y is 1-4/7=5/7 chance.
Does the median represent the center of the data? A. The median represents the center. B. The median does not represent the center because it is the smallest data value. C. The median does not represent the center because it is the largest data value. D. The median does not represent the center because it is not a data value. E. There is no median age
Answer:
A. The median represents the center.
Step-by-step explanation:
In statistics and probability theory, the median value is the middle value or center value in a group of data values or numbers. To find the median, the values have to be placed in value order, from smallest to largest. The center number would be the median. The number lies between the higher half and the lower half. Therefore the median represents the center of the data values.
Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x)
Answer:
2.25
Step-by-step explanation:
The computation of the number c that satisfied is shown below:
Given that
[tex]f(x) = \sqrt{x}[/tex]
Interval = (0,9)
According to the Rolle's mean value theorem,
If f(x) is continuous in {a,b) and it is distinct also
And, f(a) ≠ f(b) so its existance should be at least one value
i.e
[tex]f^i(c) = \frac{f(b) - f(a)}{b -a }[/tex]
After this,
[tex]f(x) = \sqrt{x} \\\\ f^i(x) = \frac{1}{2}x ^{\frac{1}{2} - 1} \\\\ = \frac{1}{2}x ^{\frac{-1}{2}[/tex]
[tex]f^i(x) = \frac{1}{{2}\sqrt{x} } = f^i(c) = \frac{1}{{2}\sqrt{c} } \\\\\a = 0, f (a) = f(o) = \sqrt{0} = 0 \\\\\ b = 9 , f (b) = f(a) = \sqrt{9} = 3\\[/tex]
After this,
Put the values of a and b to the above equation
[tex]f^i(c) = \frac{f(b) - f(a)}{b - a} \\\\ \frac{1}{{2}\sqrt{c} } = \frac{3 -0}{9-0} \\\\ \frac{1}{\sqrt[2]{c} } = \frac{3}{9} \\\\ \frac{1}{\sqrt[2]{c} } = \frac{1}{3} \\\\ \sqrt[2]{c} = 3\\\\\sqrt{c} = \frac{3}{2} \\\\ c = \frac{9}{4}[/tex]
= 2.25
PLEASE ANSWER QUICK A manufacturing facility pays its employees an average wage of $4.50 an hour with a standard deviation of 50cents. If the wages are normally distributed, what is the percentage of workers getting paid between #3.75 and $5.00 an hour? A. 80.4% B.77.4% C.70.5% D.65.4%
Answer:
B.77.4%
Step-by-step explanation:
Mean wage (μ) = $4.50
Standard deviation (σ) = $0.50
For nay given salary X, the z-score is given by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = $3.75, the z-score is:
[tex]z=\frac{3.75-4.50}{0.50}\\z=-1.5[/tex]
For X = $5.00, the z-score is:
[tex]z=\frac{5.00-4.50}{0.50}\\z=1[/tex]
A z-score of -1.5 corresponds to the 6.68th percentile, while a score of 1 corresponds to the 84.13th percentile. Therefore, the percentage of workers getting paid between $3.75 and $5.00 an hour is:
[tex]P=84.13-6.68\\P=77.45\%[/tex]
The answer is alternative B.77.4%
Solve for x. Answer as an integer or simplified fraction. Please include steps. Thanks!
Answer:
x=40 degreesStep-by-step explanation:
According to the angle sum theorem, the interior angles of a triangle add up to 180 degrees:
So, we can use the following equation to find x:
x+(x+10)+(210-3x)=180
now add like terms:
x+x+(-3x)+10+210=180
-x+220=180
now isolate the variable:
-x=180-220
-x=-40
x=-40/-1
x=40/1
x=40
The answer is that: the measure of x is 40 degrees
objective: central limit theorem assumptions. the factor(s) to be considered when assessing if the central theorem holds is/are
Answer:
Sample size
Step-by-step explanation:
Central Limit Theorem states that population with mean and standard deviation and if the sample size is large then the distribution of sample mean will be will be normally distributed. The central limit theorem holds assumptions that the factors to be considered when assessing central limit theorem is sample size.
The CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.
It is given that the objective that central limit theorem assumptions. the factor(s) to be considered when assessing if the central theorem holds.
It is required to describe the above theorem.
What is the central limit theorem?It is defined as the in statistics the assumption holds that the sample means distribution of arbitrary variables follows a normal distribution or close to normal distribution if the sample size is big.
We have an objective:
The CLT is the factor to be considered when assessing if the CLT holds a large sample size.
If we draw the random sample data and its measures, the Central limit theorem explains the distribution will explain the normal bell curve, the mean of the parameters and the distribution will be the same.
Thus, the CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.
Learn more about the Central limit theorem here:
https://brainly.com/question/5027686
6th grade math help me, please :)
Answer:
B. 168 students
Step-by-step explanation:
Given that there are a total of 600 students.
28% of the students pack their lunch.
To find:
Total number of students who pack their lunch = ?
Solution:
Percentage of a given number is calculated using the following method.
[tex]y\%[/tex] of a number [tex]x[/tex] is given by:
[tex]x \times \dfrac{y}{100}[/tex]
i.e. multiply the number by percentage to be found and divide by 100.
So, we have to find 28% of 600 here, to find the answer to the question.
[tex]\therefore[/tex] Number of students who pack their lunch is given as: (Multiply the given number 600 with 28 and divide by 100.)
[tex]600 \times \dfrac{28}{100}\\\Rightarrow 6 \times 28\\\Rightarrow \bold{168}[/tex]
So, the correct answer is:
B. 168
The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations?
(a) n 15 t 1.66 a 0.05
A. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
B. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
C. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
D. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(b) n 15 t 1.66 a 0.05
Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(c) n 26, t 2.55 a 0.01
A. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
B. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
C. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
D. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(d) n 26, t 3.95
A. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
B. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
C. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
D. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
C
b
C
c
C
d
A
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 0.5 \ in[/tex]
Generally the Null hypothesis is [tex]H_o : \mu = 0. 5 \ in[/tex]
The Alternative hypothesis is [tex]H_a : \mu \ne 0.5 \ in[/tex]
Considering the parameter given for part a
The sample size is n = 15
The test statistics is t = 1.66
The level of significance [tex]\alpha = 0.05[/tex]
The degree of freedom is evaluated as
[tex]df = n- 1[/tex]
[tex]df = 15- 1[/tex]
[tex]df = 14[/tex]
Using the critical value calculator at (social science statistics web site )
[tex]t_{\frac{\alpha}{2} ,df } = t_{\frac{0.05 }{2} ,14} = 2.145[/tex]
We are making use of this [tex]t_{\frac{\alpha }{2} }[/tex] because it is a one-tail test
Looking at the value of t and [tex]t_{\frac{\alpha }{2} }[/tex] the we see that [tex]t < t_{\frac{\alpha }{2} }[/tex] so the null hypothesis would not be rejected
Considering the parameter given for part b
The sample size is n = 15
The test statistics is t = -1.66
The level of significance [tex]\alpha = 0.05[/tex]
The degree of freedom is evaluated as
[tex]df = n- 1[/tex]
[tex]df = 15- 1[/tex]
[tex]df = 14[/tex]
Using the critical value calculator at (social science statistics web site )
[tex]t_{\frac{\alpha}{2} ,df } = t_{\frac{0.05 }{2} ,14} = -2.145[/tex]
Looking at the value of t and [tex]t_{\frac{\alpha}{2} ,df }[/tex] the we see that t does not lie in the area covered by [tex]t_{\frac{\alpha}{2} , df }[/tex] (i.e the area from -2.145 downwards on the normal distribution curve ) hence we fail to reject the null hypothesis
Considering the parameter given for part c
The sample size is n = 26
The test statistics is t = -2.55
The level of significance [tex]\alpha = 0.01[/tex]
The degree of freedom is evaluated as
[tex]df = n- 1[/tex]
[tex]df = 26- 1[/tex]
[tex]df = 25[/tex]
Using the critical value calculator at (social science statistics web site )
[tex]t_{\frac{\alpha}{2} ,df } = t_{\frac{0.01 }{2} ,25} = 2.787[/tex]
Looking at the value of t and [tex]t_{\frac{\alpha }{2} }[/tex] the we see that t does not lie in the area covered by [tex]t_{\alpha , df }[/tex] (i.e the area from -2.787 downwards on the normal distribution curve ) hence we fail to reject the null hypothesis
Considering the parameter given for part d
The sample size is n = 26
The test statistics is t = -3.95
The level of significance [tex]\alpha = 0.01[/tex]
The degree of freedom is evaluated as
[tex]df = n- 1[/tex]
[tex]df = 26- 1[/tex]
[tex]df = 25[/tex]
Using the critical value calculator at (social science statistics web site )
[tex]t_{\frac{\alpha}{2} ,df } = t_{\frac{0.01 }{2} ,25} = -2.787[/tex]
Looking at the value of t and [tex]t_{\frac{\alpha}{2} }[/tex] the we see that t lies in the area covered by [tex]t_{\alpha , df }[/tex] (i.e the area from -2.787 downwards on the normal distribution curve ) hence we reject the null hypothesis
A necklace was on sale for 20% discount off the original price of
$1250.00. What was the final sale price if 12.5% VAT has to be
paid?
Answer:
= $ [tex] \mathsf{1125}[/tex]Step-by-step explanation:
[tex] \mathrm{Given}[/tex],
[tex] \mathrm{Discount\% = 20\%}[/tex]
[tex] \mathrm{Marked \: price = 1250}[/tex]
[tex] \mathrm{Now \: let's \: find \: the \: discount \: amount}[/tex]
[tex] \mathrm{discount \: amount = dis\% \: of \: MP}[/tex]
[tex] \mathrm { = 20\% \: of \: 1250}[/tex]
[tex] \mathrm{ = 250}[/tex]
[tex] \mathrm{let's \: find \: the \: selling \: price}[/tex]
[tex] \mathrm{ = MP \: - \: discount \: amount}[/tex]
[tex] \mathrm{ = 1250 - 250}[/tex]
= $ [tex] \mathrm{1000}[/tex]
[tex] \mathrm{lets \: find \: the \: Vat \: amount}[/tex]
[tex] \mathrm{vat \: amount = vat\% \: of \: sp}[/tex]
[tex] \mathrm{ = 12.5\% \: of \: 1000}[/tex]
= $ [tex] \mathrm{ 125}[/tex]
[tex] \mathrm{Now \: finally \: let's \: find \: the \: selling \: price \: with \: vat}[/tex]
[tex] \mathrm{selling \: price \: + \: vat \: amount}[/tex]
[tex] \mathrm{ = 1000 + 125}[/tex]
= $ [tex] \mathrm{1125}[/tex]
Therefore, The final sale of the necklace is $ 1125
Hope I helped
Best regards!
use the substitution method to solve the system of equation.s choose the correct ordered pair y=6x-4 y=x -7
Answer:
x=-3/5 and y=-38/5
Step-by-step explanation:
y=6x-4
y= x -7 substitute y=6x-4
6x-4=x-7
6x-x=-7+4
5x=-3
x=-3/5 ( substitute for x in y=6x-4)
y=6(-3/5)-4
y=-18/5-4
y=(-18-20)/5= -38/5
Determine whether the following sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative. A researcher wishes to compare of and She obtains a random sample of who and determines each Determine whether the following sampling is dependent or independent. A. B. The sampling is independent because an individual selected for one sample does dictate which individual is to be in the second sample. C. The sampling is dependent because an individual selected for one sample does not dictate which individual is to be in the second sample. D. Indicate whether the response variable is qualitative or quantitative. A. The variable is because it . B. The variable is because it . C. The variable is because it . D. The variable is because it .
Answer:
The sampling is dependent because an individual selected for one sample does dictate about which individual to be selected in the second sample.
The variable is qualitative because it classifies the individual.
Step-by-step explanation:
The sample is dependent as the second individual selected in the sample is dependent on the first individual selection. The sample selection is not random and is dictated. The variables selected are qualitative in nature because they identify the quality of response variable which is non numerical in nature.
There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. b How many ways can we choose a Senator from a chosen state? c How many ways can the 3-Senator committee be formed such that no two Senators are from the same state?
Answer:
a) rCn = 1176
b) 2352
Step-by-step explanation:
a)Each committee should be formed with 3 members ( no two members could be of the same state) then
Let´s fix a senator for any of the 50 states so in the new condition we need to combined 49 senators in groups of 2 then
rCn = n! / (n - r )! *r!
rCn = 49!/ (49 - 2)!*2!
rCn = 49*48*47! / 47!*2!
rCn = 49*48 /2
rCn = 1176
So we can choose in 1176 different ways a senator for a given state
b) To answer this question we have to note, that, 1176 is the number of ways a committee can be formed with senators of different sate (taking just one senator for state ) if we have 2 senators we need to multiply that figure by 2.
1176*2 = 2352
(I NEED HELP) The data below shows the scores of some students on a test: 23, 27, 21, 20, 25, 31, 22 Which box-and-whisker plot represents the data?
Answer:
B
Step-by-step explanation:
Answer:
the 2nd one
Step-by-step explanation:
because the Minimum is 20
the Maximum is 31
the median is 23
20, 21, 22, 23, 25, 27, 31,
21, 22, 23, 25, 27
22, 23, 25,
23
Find exact value of cos
Work Shown:
[tex]\sin^2 \theta + \cos^2 \theta = 1\\\\\left(\frac{3}{10}\right)^2 + \cos^2 \theta = 1\\\\\frac{9}{100} + \cos^2 \theta = 1\\\\\cos^2 \theta = 1 - \frac{9}{100}\\\\\cos^2 \theta = \frac{100}{100}-\frac{9}{100}\\\\\cos^2 \theta = \frac{91}{100}\\\\\cos \theta = \sqrt{\frac{91}{100}} \ \text{ cosine positive in Q1}\\\\\cos \theta = \frac{\sqrt{91}}{\sqrt{100}}\\\\\cos \theta = \frac{\sqrt{91}}{10}\\\\[/tex]
Answer:
√91/10
Step-by-step explanation:
sin 0.3 is equal to 18(approximate value)
cos18°=0.951
which is √91/10
Find the value of EB
Answer:
31Step-by-step explanation:
Given,
AD = 38
EB = 7x - 4
FC = 6x - 6
Now, we have to find the value of X
[tex]eb \: = \frac{1}{2} (ad \: + fc \: )[/tex] ( Mid segment Theorem )
Plug the values
[tex]7x - 4 = \frac{1}{2} (38 + 6x - 6)[/tex]
Calculate the difference
[tex]7x - 4 = \frac{1}{2} (32 + 6x)[/tex]
Remove the parentheses
[tex]7x - 4 = \frac{32}{2} + \frac{6x}{2} [/tex]
[tex]7x - 4 = 16 + 3x[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex]7x - 3x = 16 + 4[/tex]
Collect like terms
[tex]4x = 16 + 4[/tex]
Calculate the sum
[tex]4x = 20[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{20}{4} [/tex]
Calculate
[tex]x = 5[/tex]
The value of X is 5
Now, let's find the value of EB
EB = 7x - 4
Plug the value of X
[tex] = 7 \times 5 - 4[/tex]
Calculate the product
[tex] = 35 - 4[/tex]
Calculate the difference
[tex] = 31[/tex]
The value of EB is 31
Hope this helps..
Best regards!!
What is the difference of the rational expressions below?
6/x - 5x/x+2
A.
5x + 6
2
O
B. 5x + 6x +12
** + 2x
O
c.
5x6
2x+2
D. 5x' +6x +12
2x + 2
The difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).
Thus, the correct option would be:
C. (x + 12)/(x(x+2))
To find the difference of the rational expressions, we need to subtract the second expression from the first expression.
Let's simplify the expressions first:
The first expression is 6/x - 5x/(x+2).
To combine the terms, we need a common denominator, which is (x)(x+2).
Converting the first term, 6/x, to have a denominator of (x)(x+2), we get (6(x+2))/(x(x+2)).
Now, we can combine the terms:
[(6(x+2))/(x(x+2))] - [5x/(x+2)]
To subtract the fractions, we need to have a common denominator, which is (x)(x+2).
Expanding the numerators, we get:
[(6x + 12)/(x(x+2))] - [5x/(x+2)]
Now, we can subtract the fractions:
[(6x + 12 - 5x)/(x(x+2))]
Simplifying the numerator, we have:
(6x - 5x + 12)/(x(x+2))
Combining like terms, we get:
(x + 12)/(x(x+2))
Therefore, the difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).
Thus, the correct option would be:
C. (x + 12)/(x(x+2))
For similar question on rational expressions.
https://brainly.com/question/29061047
#SPJ8
Help please!! Thank you
Answer:
D. 6
Step-by-step explanation:
here, as given set Q consists { 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36}
and set Z contains {3, 6, 9, 12, 15, 18, 21,24, 27, 30, 33, 36, .... }
so be comparing both, we can see that the numbers 6, 12, 18, 24, 30 and 36 is repeated.
What is the greatest prime you must consider to test whether 7066 is prime?
Answer:
Step-by-step explanation:
The square root of 7066 is 84.0595....
Therefore the largest number we must test is 84, seeing as now we have proven we do not need to test any numbers greater than 84.0595...
That means, we only need to test prime numbers smaller than 84 to see if they go into 7066.
84 isn't prime. But 83 is prime.
Therefore, the greatest prime that needs to be considered for divisibility is 83.
Answer:
The numbers 7066 is not prime .
But we easily know when a number is prime when we divide it by the first prime numbers; 2, 3, 5, 7, 11.
Step-by-step explanation:
It is known with certainty that a number is prime when it is only divisible by and by unity.
But in this case, that number, when divided by other numbers less than the one, shows that when dividing into the remainder, it gives zero, which means that it is not only divisible by itself or by the unit, but also by other numbers.
for example; 7066/2=3533 , the remainder is zero;
If $y^2= 36$, what is the greatest possible value of $y^3$?
Answer:
The greatest possible value of [tex]y^3=216[/tex]
Step-by-step explanation:
We have the statement [tex]y^2=36[/tex], and we have to find the greatest possible value of [tex]y^3[/tex], first we need to find the value of y.
[tex]y^2=36[/tex], to get the y by itself on the left side, we need to take the square root of both sides. [tex]\sqrt{y^2} =\sqrt{36}[/tex] The square root of [tex]y^2[/tex] is y, because y*y = [tex]y^2[/tex], and the square root of 36 is 6 or -6.
We now need to find the greatest value of [tex]y^3[/tex]. When we plug in 6 to [tex]y^3[/tex], we get positive 216, and when we plug in -6, we get -216. We need to find the greatest possible value, so in this case we compare 216 and -216, 216 is greater than -216, so the answer would be positive 216.
Answer:
216
Step-by-step explanation:
If y² = 36, then y is 6 or -6. When y = 6, we have y³ = 6³ = 216. When y = -6, we have y³ = (-6)³ = -216. The greatest possible value of y³ is 216.
If 5e^x=300, x
I need help fast
Answer:
ln(60)
Step-by-step explanation:
We have the equation [tex]5e^x=300[/tex]. We can divide both sides of the equation by 5, getting [tex]e^x=60[/tex]. Finally, we can take the natural log of both sides, getting that x is equal to [tex]\ln(60)[/tex].
Identify an equation in point-slope form for the line perpendicular to
y= - 1/3x - 6 that passes through (-1,5).
O A. y + 1 = 3(x - 5)
O B. y + 5 = 1/3(x - 1)
O C. y - 5 = 3(x + 1)
O D. y - 5 = - 1/3(x + 1)
Answer:
hope you get it....sorry for any mistake calculations
A certain medicine is given in an amount proportional to patient’s body weight. Suppose a patient weigh in 116 pounds requires 126 mg of medicine. What is the amount of medicine required by patient way and 174 pounds?
Answer: 189 mg.
Step-by-step explanation:
Let x be the weight of the body( in pounds) and y be the amount of medicine( in mg).
Given: A certain medicine is given in an amount proportional to patient’s body weight.
i.e. [tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
Let [tex]x_1=116\ \ \ ,\ y_1=126[/tex] , [tex]x_2=174[/tex]
then,
[tex]\dfrac{116}{126}=\dfrac{174}{y_2}[/tex]
[tex]\Rightarrow\ y_2=\dfrac{174\times126}{116}\\\\\Rightarrow\ y_2=189[/tex]
Hence, he amount of medicine required by patient weighing 174 pounds = 189 mg.
A group of children is trying to share a pile of stickers. If every
child gets two stickers, there will be 7 stickers left over. If two
children do not get any stickers, then each of the remaining
children will get exactly 3 stickers.
How many children are in the group?
Answer:
7 children
Step-by-step explanation:
Answer:
7 children is the correct answer
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Can anyone help? I am stuck. Find m∠G.
Answer:
80
Step-by-step explanation:
The quadrilateral is a kite.
The angle opposite to angle H is equal to angle H.
Angle F = 110 degrees
Angles in a quadrilateral add up to 360 degrees.
60 + 110 + 110 + G = 360
280 + G = 360
G = 360 - 280
G = 80
The measure of angle G is 80 degrees.
Answer: 80 degrees.
Step-by-step explanation:
In a kite, the angles formed by noncongruent sides are congruent. Thus, <EFG is 110 degrees. Then, because a kite is a quadrilateral, all of the angles in it add up to 360. Thus, is <FGH = x, then 110+110+60+x=360. Thus, x = 80.
Hope it helps <3
6th grade math , help me please :)
Answer:
(a) 3:5
(b) 15
Step-by-step explanation:
Well first we need to create a ratio for the 5 shades squares and 3 non+shaded squares.
It is asking for unshaded first so our ratio will be,
3:5
(a) 3:5
So if there is 9 unshaded how many shaded is there.
Well we can just make the following ratio 9:x
So 9/3 = 3
Meaning 3*5 = 15
So x = 15
(b) 15
Answer:
a) 3/5
b) 15
Step-by-step explanation:
(a)
unshaded: 3
shaded: 5
unshaded to shaded: 3/5
(b)
There are now 3 unshaded squares. You need 9 unshaded squares, so you need to have three times as many total squares as you have now.
Add two more lines just like the given line.
Each new line will have 5 shaded and 3 unshaded squares.
Now you have a total of 9 unshaded and 15 shaded squares.
Enter a range of values of x
Answer:
[tex]-5<x<26[/tex].
Step-by-step explanation:
We know that if two corresponding sides of two triangles are equal, then third sides of the triangles depend on angle between equal sides.
Angle opposite to larger side is larger.
Since, 14 < 15, therefore
[tex]2x+10<62[/tex]
[tex]2x<62-10[/tex]
[tex]2x<52[/tex]
[tex]x<26[/tex] ...(1)
We know that, angle can not not negative.
[tex]2x+10>0[/tex]
[tex]2x>-10[/tex]
[tex]x>-5[/tex] ...(2)
From (1) and (2), we get
[tex]-5<x<26[/tex]
Therefore, the range of values of x is [tex]-5<x<26[/tex].
determining probability of events. please help!