Answer:
[tex]x = \sqrt{5}\\\\y = \frac{15}{ \sqrt{5} }[/tex]
Step-by-step explanation:
According to the information of the problem
[tex]xy = 15[/tex]
And
[tex]S = 3x+y[/tex]
If you solve for [tex]y[/tex] on the first equation you get that
[tex]y = {\displaystyle \frac{15}{x}}[/tex]
then you have that
[tex]S = {\displaystyle 3x + \frac{15}{x} }[/tex]
If you find the derivative of the function you get that
[tex]S' = {\displaystyle 3 - \frac{15}{x^2}} = 0\\[/tex]
The equation has two possible solutions but you are looking for POSITIVE numbers that make [tex]S[/tex] as small as possible.
Then
[tex]x = \sqrt{5}\\\\y = \frac{15}{ \sqrt{5} }[/tex]
What is the slope, m, and y-intercept for the line that is plotted on the grid below? On a coordinate plane, a line goes through points (0, 4) and (negative 2, 0). m = One-half, (0, –2) m = One-half, (0, 4) m = 2, (0, –2) m = 2, (0, 4)
Answer:
D. m = 2, (0, 4)
Step-by-step explanation:
the answer is D
I got it write on the quiz
Answer:
yes it is D :D
Step-by-step explanation:
A movie complex is showing the same movie in three theatres. In theatre A, 112 of the 160 seats are filled. In theatre B, 84 seats are filled and 56 are empty. In theatre C, 63 of the 180 seats are empty. Which theatre has the greatest percent of seats filled?
Answer:
a
Step-by-step explanation:
bc it does. and it has the highest percentage of it
x² + y² − 10x + 6y − 47 = 0.
Select one:
A. center: (−4, −3); radius: 5
B. center: (5, −3); radius: 9
C. center: (−2, 5); radius: 3
D. center: (1, 3); radius: 9
what are the properties of parallelogram
Answer:
The properties of the parallelogram are simply those things that are true about it. These properties concern its sides, angles, and diagonals.
Step-by-step explanation:
The parallelogram has the following properties:
Opposite sides are parallel by definition.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
The diagonals bisect each other.
If you just look at a parallelogram, the things that look true (namely, the things on this list) are true and are thus properties, and the things that don’t look like they’re true aren’t properties.
If you draw a picture to help you
when I was six my brother was half my age. next year if I turn 40 how old will my brother be?
Answer:
37
Step-by-step explanation:
You were 6 and he was half which made him 3
So you’re gonna turn 40 he’s gonna be three years younger than you which is 37
Hope I helped
What is the point-slope form of a line with slope 2/5 that contains the point (-3, 6)?
O A. y-6= -2/5(x+3)
O B. y+6 = 2/5(x+3)
O C. y-6 = 2/5(x+3)
O D.y-3 = 2/5(x+3)
Answer:
y -6 = 2/5(x+3)
Step-by-step explanation:
The point slope form of an equation is
y -y1 = m(x-x1)
where m is the slope and (x1,y1) is the point
y -6 = 2/5(x- -3)
y -6 = 2/5(x+3)
C.) y - 6 = 2/5(x + 3)
The original point slope equation is the following
[tex]y - y_1 = m(x-x_1)[/tex]
When you plug in negative point values into this equation, the sign changes from '-' to '+'. This is how you can determine which equation accurately represents the line.
Lindsay Electronics, a small manufacturer of electronic research equipment, has approximately 6 comma 500 items in its inventory and has hired Joan Blasco-Paul to manage its inventory. Joan has determined that 11% of the items in inventory are A items, 33% are B items, and 56% are C items. She would like to set up a system in which all A items are counted monthly (every 20 working days), all B items are counted quarterly (every 62 working days), and all C items are counted semiannually (every 121 working days). How many items need to be counted each day? The total number of items that need to be counted each day is nothing items (round your response to the nearest whole number).
Answer:
The total number of items to be counted each day ≈ 100
Step-by-step explanation:
Lindsay Electronics has 6,500 items in its inventory.
11% of the items in inventory are A items
33% of the items in inventory are B items
56% of the items in inventory are C items
A items are counted every 20 working days
B items are counted every 62 working days
C items are counted every 121 working days
How many items need to be counted each day?
First we will find the number of items of type A, B and C
Number of A items = 11% of 6,500 = 0.11*6500 = 715
Number of B items = 33% of 6,500 = 0.33*6500 = 2145
Number of C items = 56% of 6,500 = 0.56*6500 = 3640
The number of A items to be counted each day is
A items = 715/20
The number of B items to be counted each day is
B items = 2145/62
The number of C items to be counted each day is
C items = 3640/121
The total number of items to be counted each day is
Total items = 715/20 + 2145/62 + 3640/121
Total items = 100.42
Rounding the answer to the nearest whole number yields,
Total items ≈ 100
The last day we were in school was March 13. There are 180 days in a school year.
1. How many total days of school have we missed as of today?
2. What percentage of days were we in school this year?
Is this qusioun as of today may 18?
Based on the dates given, you missed approximately 90 days of school. If your school year usually starts around August 25, you were in school for about 170 days out of a 180-day school year. That means you were in school for approximately 94.44% of the year.
Explanation:To solve this question, first, we need to find the number of days missed. You mentioned your last day in school was March 13. Assuming today's date is June 13, that is approximately 3 months. As each month has about 30 days, then 3 months would total about 90 days missed from school. To summarize:
Last school day: March 13Today's date: June 13Total days missed: Approximately 90The second part of the question requires us to find the percentage of days you were in school. You mentioned that there are 180 school days in a year. If the last day was on March 13 and the school year usually begins around August 25, that would make approximately 170 days in school before the school closures. So, the calculation would be (170/180)*100% = approximately 94.44%. Hence, you were in school for approximately 94.44% of the year.
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Luther takes 45 bottles of water on a camping trip. If he drinks 80 % of them how many does he have left?
Answer:
9
Step-by-step explanation:
80% of 45 is 36
45-36=9
The value of the coefficient of correlation ( r) a. can never be equal to the value of the coefficient of determination (r2). b. is always larger than the value of the coefficient of determination (r2). c. is always smaller than the value of the coefficient of determination (r2). d. can be equal to the value of the coefficient of determination (r2).
Answer:
d. can be equal to the value of the coefficient of determination (r2).
True on the special case when r =1 we have that [tex] r^2 = 1[/tex]
Step-by-step explanation:
We need to remember that the correlation coefficient is a measure to analyze the goodness of fit for a model and is given by:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
The determination coefficient is given by [tex] R= r^2[/tex]
Let's analyze one by one the possible options:
a. can never be equal to the value of the coefficient of determination (r2).
False if r = 1 then [tex] r^2 = 1[/tex]
b. is always larger than the value of the coefficient of determination (r2).
False not always if r= 1 we have that [tex] r^2 =1[/tex] and we don't satisfy the condition
c. is always smaller than the value of the coefficient of determination (r2).
False again if r =1 then we have [tex] r^2 = 1[/tex] and we don't satisfy the condition
d. can be equal to the value of the coefficient of determination (r2).
True on the special case when r =1 we have that [tex] r^2 = 1[/tex]
The correct answer is d. can be equal to the value of the coefficient of determination (r²).
The coefficient of correlation (r) and the coefficient of determination (r²) are related statistical measures used to describe the strength and direction of the linear relationship between two variables.
The coefficient of correlation (r) quantifies the strength and direction of this linear relationship, ranging from -1 to 1, where -1 represents a perfect negative correlation, 1 represents a perfect positive correlation, and 0 represents no linear correlation.
On the other hand, the coefficient of determination (r²) is simply the square of the coefficient of correlation and represents the proportion of variance in one variable that can be explained by the linear relationship with the other variable.
Since r² is the square of r, it's entirely possible for them to be equal. In fact, when r is either 1 or -1 (perfect correlations), r² will be equal to 1, indicating that 100% of the variance in one variable is explained by the linear relationship with the other variable.
Similarly, when r is 0 (no linear correlation), r² will be equal to 0, indicating that none of the variance in one variable is explained by the linear relationship with the other variable.
So, the relationship between r and r² depends on the strength of the linear correlation, and they can indeed be equal under certain conditions.
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A well-known battery manufacturer claims its product lasts at least 5000 hours, on average. If a sample of 81 batteries has an average lifetime of 4917.5 hours with a standard deviation of 450 hours, use the critical value approach to determine whether you reject or not reject the null hypothesis at a 5% level of significance. What does this mean in terms of the manufacturer's claim
Answer:
[tex]t=\frac{4917.5-5000}{\frac{450}{\sqrt{81}}}=-1.65[/tex]
The degrees of freedom for this case are:
[tex]df=n-1=81-1=80[/tex]
We need to find a critical value in the t distribution with 80 degrees of freedom who accumulates 0.05 of the area in the left and we got:
[tex] t_{cric}= -1.664[/tex]
Since the calculated value is not less than the critical value we don't have enough evidence to conlcude that the true mean is significantly lower than 5000 hours. Then the claim by the manufacturer (product lasts at least 5000 hours) makes sense.
Step-by-step explanation:
Information given
[tex]\bar X=4917.5[/tex] represent the sample mean
[tex]s=450[/tex] represent the sample standard deviation
[tex]n=81[/tex] sample size
[tex]\mu_o =5000[/tex] represent the value to check
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic (variable of interest)
System of hypothesis
We want to determine if product lasts at least 5000 hours, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 5000[/tex]
Alternative hypothesis:[tex]\mu < 5000[/tex]
The statistic for a one sample t testo for the true mean is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{4917.5-5000}{\frac{450}{\sqrt{81}}}=-1.65[/tex]
The degrees of freedom for this case are:
[tex]df=n-1=81-1=80[/tex]
We need to find a critical value in the t distribution with 80 degrees of freedom who accumulates 0.05 of the area in the left and we got:
[tex] t_{cric}= -1.664[/tex]
Since the calculated value is not less than the critical value we don't have enough evidence to conlcude that the true mean is significantly lower than 5000 hours. Then the claim by the manufacturer (product lasts at least 5000 hours) makes sense.
if a pack of 12 pencils cost $1.29 how much does a single pencil cost
Answer:
$0.11 (2 d.p.)
Step-by-step explanation:
Please see the attached picture for the full solution.
The cost of one pencil is 10.75 cents.
First, convert the total cost from dollars to cents.
As we know,
Since $1.29 is equal to 129 cents:
$1.29 * 100
= 129 cents.
Next,
divide 129 cents by 12 pencils to find the cost per pencil:
129 cents / 12 pencils
= 10.75 cents.
So, the cost of one pencil is 10.75 cents.
Removing which point from the coordinate plane would make the graph a function of X?
What’s the correct answer for this?
Answer:
D.
Step-by-step explanation:
Density = mass / volume
Density= 3 , mass = 80
3 = 80 / volume
Volume = 80 / 3
Volume = 26.67 cubic inch
Now volume of a cube= 3 (side length)
26.67 = 3(side length)
Side length=26.67 /3
Side length=8.89 inches
Side length ≈ 9 inches
How much larger is a pizza in 18-in square pizza pan than a pizza made in a 18-in diameter circular pan? Use 3.14 for pi
The 18-inch square pizza is 69.66 square inches larger than the 18-inch diameter circular pizza. This calculation is done by finding the areas of both the square and the circle and then subtracting the circular area from the square one.
Explanation:The subject of this question is Mathematics, specifically dealing with the comparison of areas of geometric shapes, and the problem seems to be aimed at a middle school level. To find out how much larger a square pizza is compared to a circular pizza, we will calculate the area of both shapes and then compare the two.
The area of the square pizza is straightforward since the length of a side is given as 18 inches. The formula for the area of a square is A = a², so:
Area of square pizza = 18 in × 18 in = 324 in².
Next, let's calculate the area of the circular pizza using the formula: A = πr², where r is the radius. The diameter is given as 18 inches, so the radius (r) is half of the diameter, which is 9 inches. Using 3.14 for π, we find:
Area of circular pizza = 3.14 × 9 in × 9 in = 3.14 × 81 in² = 254.34 in².
To find the difference in areas, we subtract the area of the circular pizza from the area of the square pizza:
Difference in areas = 324 in² - 254.34 in² = 69.66 in².
Therefore, an 18-inch square pizza is 69.66 square inches larger than an 18-inch diameter circular pizza.
The sum of 2ab^2 and (-5ab^2) is the same as the sum of (-6ab^2) and
Answer:
? = 3ab^2
for the sum of (-6ab^2) and 3ab^2
Step-by-step explanation:
2ab^2 +(-5ab^2) =(-6ab^2) + ?
-3ab^2 = -6ab^2 + ?
? = 6ab^2 - 3ab^2
? = 3ab^2
Paul works out with 3 weights that are each 2.5 kilograms each. What is the total mass of the 2.5 kilogram weights in grams
Answer:
750000
Step-by-step explanation:
3 times 2.5 = 7.5 then to convert to grams times by 1000 which is 750000
Will the sugar, the sand, or both dissolve in the water?
Answer:
sugar
Step-by-step explanation:
Answer:
Sugar will dissolve
Step-by-step explanation:
Sand does not dissolve in water, but it absorbs water to some extent
What is the explicit formula for this geometric sequence?
8,4, 2, 1, ...
Answer:
[tex]a_{n}[/tex] = 8 *[tex]0.5^{n-1}[/tex]
Step-by-step explanation:
First find the common ratio
r = 4/8 = 1/2
and first term is 8
a_n = a_1 * r^(n-1)
a_n = 8 * (1/2)^(n-1)
[tex]a_{n}[/tex] = 8 *[tex]0.5^{n-1}[/tex]
The picture below is of a Little League Baseball field. The distance from Home Plate to First Base is 60 feet, and from Home Plate to the center of the Pitcher’s Mound is 46 feet. The baseball "diamond" is actually a square (distance between each base is 60 feet), so the angle made by each base is 90°. So, if a line were connecting Home Plate with the Pitcher’s mound, it would create a 45° angle. So, approximately how far is First Base from the center of the Pitcher’s Mound? (HINT: The pitcher’s mound is not in the middle of the field, so there are NO right angles in this problem.) (
Answer:
42.58 FT
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Answer:
While chalking the lines on a little league baseball field, Tory determined that the distance between each of the bases is 45 feet. What would be the approximate distance from home plate to second base be if measured through the pitchers mound?
Step-by-step explanation:
42.58
What is the approximate difference in tenths between StartRoot 12 EndRoot and StartRoot 15 EndRoot? 0.2 0.4 1.5 1.7
Final answer:
The approximate difference in tenths between the square roots of 12 and 15 is 0.4. This is found by approximating the square roots (3.46 and 3.87, respectively) and subtracting the smaller from the larger.
Explanation:
The student asks for the approximate difference in tenths between StartRoot 12 EndRoot and StartRoot 15 EndRoot. To find the square roots we can use a calculator or estimate:
Square root of 12 is approximately 3.46.
Square root of 15 is approximately 3.87.
Now find the difference:
3.87 - 3.46 = 0.41
0.4 is the approximate difference in tenths between the square roots of 12 and 15. The options given are 0.2, 0.4, 1.5, and 1.7. Therefore, the closest value to our calculation is 0.4.
Find the distance between (3, 24) and (7,
56).
Answer:
Square root of 1040.
Or decimal form - 32.249
Step-by-step explanation:
What are the dimensions of the cross section formed by
a plane intersecting this rectangular prism parallel to its
base?
The cross section is a
The length of the cross section is
The width of the cross section is
cm.
cm.
ith = 4 cm
Answer:
rectangle, 5,4
Step-by-step explanation:
i just did the assignment and got it right
about how many liters of water can the large jug hold
Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a service facility. Suppose they are normal random variables with means of 50 minutes, 60 minutes, and 40 minutes, respectively. The standard deviations are 15 minutes, 20 minutes, and 10 minutes, respectively. a Suppose X1, X2, and X3 are independent. All three repairs must be completed on a given object. What is the mean and variance of the total repair time for this object.
Answer:
The mean of the total repair time is 150 minutes.
The variance of the total repair time is 725 minutes^2.
Step-by-step explanation:
To solve this problem, we have to use the properties of the mean and the variance. Our random variable is the sum of 3 normal variables.
In the case, for the mean, we have that the mean of the sum of 3 normal variables is equal to the sum of the mean of the 3 variables:
[tex]y=x_1+x_2+x_3 \\\\E(y)=E(x_1+x_2+x_3)=E(x_1)+E(x_2)+E(x_3)\\\\E(y)=50+60+40=150[/tex]
For the variance, we apply the property for the sum of independent variables (the correlation between the variables is 0):
[tex]V(y)=V(x_1)+V(x_2)+V(x_3)\\\\V(y)=s_1^2+s_2^2+s_3^2\\\\V(y)=15^2+20^2+10^2\\\\V(y)=225+400+100\\\\V(y)=725[/tex]
Write 2 ones and 5 hundredths as a decimal
Answer:
2.05
Step-by-step explanation:
Look at this chart
2 ones and 5 hundredths can be written as 2.05 in decimal form.
What are decimals?Decimals are values that utilize a dot known as the decimal point to distinguish between the whole number portion and the fractional portion. This dot acts as a separator marking the boundary, between these two parts of a number. The fractional section of a decimal can be expressed in units such as tenths, hundredths, thousandths and forth.
In this case the digit 2 signifies the number element of the value while 0.05 represents its fractional component. The presence of the point ensures a division, between these two segments, one being whole and the other being fractional.
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what is the surface area to a cylinder
A. 2(Pi)rh+2(Pi)r^2
B. 1/2Pl+B
C. Ph+2B
D.(Pi)rl+(Pi)r^2
E. Bh
D.(Pi)r^2h
Answer:
A. 2(Pi)rh+2(Pi)r^2
Step-by-step explanation:
The surface area of a cylinder is the sum of the lateral area and the area of the two circular ends.
The lateral area is the product of the circumference of the cylinder and its height:
lateral area = 2πrh
The area of the two ends is twice the area of each of those circles, so is ...
total end area = 2(πr²)
Then the total surface area of a cylinder is ...
SA = 2πrh +2πr²
Help me pleassseeeeeeee
I’m so confused! Please help! :)
Answer:
The answer is 18.84
Step-by-step explanation:
The diameter is 6.
Circumference = d[tex]\pi[/tex]
6 * 3.14 = 18.84
How do you know that the right triangles are the bases of the prism
Answer:
if the triangular faces are equilateral, the prism is regular, in which case the rectangular faces are congruent. The rectangular faces are said to be lateral, while the triangular faces are bases. If the bases are horizontal, they are sometimes called the top and the bottom (faces).
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Step-by-step explanation: