The solution for the inequality is 11.746 ≤ x ≤ 24.44
Kali earns a 15.75 plus a flat fee of 50 from her job.
She wants to earn between 200 and 400.
Let 'x' denote her earning potential.
Then the inequality for her earning potential is given by,
200 ≤ 15.75x + 50 ≤ 400
We solve this inequality for x.
Subtract 50 from the inequality,
⇒ 200 -15 ≤ 15.75x ≤ 400 -15
⇒ 185 ≤ 15.75x ≤ 385
Divide by 15.75,
⇒ 11.746 ≤ x ≤ 24.44
is the solution for the inequality.
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The equation of a curve is xy squared minus 2x square y squared equal 0. Find the gradient of the tangent to the curve at (1,2)?
Solution
[tex]xy^2-2x^2y^2=0[/tex]we need to find the derivative with respect to x. dy/dx
[tex]\begin{gathered} \frac{d}{dx}(xy^2-2x^2y^2=0)=\frac{d}{dx}(xy^2)-2\frac{d}{dx}(x^2y^2)=0 \\ \\ \text{ using product rule} \\ \\ \Rightarrow x\frac{d}{dx}(y^2)+y^2\frac{d}{dx}(x)-2x^2\frac{d}{dx}(y^2)+2y^2\frac{d}{dx}(x^2)=0 \\ \end{gathered}[/tex]Applying chain rule
[tex]\begin{gathered} x\cdot\frac{d}{dy}(y^2)\cdot\frac{dy}{dx}+y^2-2x^2\cdot\frac{d}{dy}(y^2)\cdot\frac{dy}{dx}+2y^2(2x)=0 \\ \\ \Rightarrow x(2y)\frac{dy}{dx}+y^2-2x^2(2y)\frac{dy}{dx}+4xy^2=0 \\ \\ \Rightarrow2xy\frac{dy}{dx}+y^2-4x^2y\frac{dy}{dx}+4xy^2=0 \\ \\ \Rightarrow(2xy-4x^2y)\frac{dy}{dx}=-y^2-4xy^2 \\ \\ \Rightarrow\frac{dy}{dx}=\frac{-(y^2+4xy^2)}{2xy-4x^2y}=\frac{y^2+4xy^2}{4x^2y-2xy} \\ \\ \Rightarrow\frac{dy}{dx}=\frac{y^{2}+4xy^{2}}{4x^{2}y-2xy} \end{gathered}[/tex]At point (1,2)
[tex]\frac{dy}{dx}=\frac{(2)^2+4(1)(2)^2}{4(1)^2(2)-2(1)(2)}=5[/tex]Using slope intercept equation
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \\ y-2=5(x-1) \\ \\ y-2=5x-5 \\ \\ \Rightarrow y=5x-5+2 \\ \\ \Rightarrow y=5x-3 \end{gathered}[/tex]help me pleaseeeeeeeeeeeeeeeeeeeeeeeee !!!
Answer:
[tex]f(x)=\frac{5}{6}x+21[/tex]
Step-by-step explanation:
Slope = 5/6
Point = (-18,6)
Using Point-Slope form
y-6=5/6(x+18)
y-6=5/6x+15
y=5/6x+21
:]
6A. Solve h(0)=100-16(0) to the 2nd power and What does the output represent 6B. Solve h(2)=100-16(2) to the 2nd power and does our equation predict that the ball has to hit the ground at 2 seconds. Explain
I think is confused
6A.- h(0) = 100 - 16(0)^2
= 100 - 0
h(0) = 100
h(0) = 100 ft
The result is the value starting height 100 ft
6B.- h(2) = 100 - 16(2)^2
h(2) = 100 - 64
h(2) = 36 ft
No, the equation does ot predict that the ball is going to hit the ground after 2 seconds because the height was 32 ft, that is the height necessary to hit the ground.
I have to send you the question
The given expression fro the sum of n terms:
[tex]\begin{gathered} S_n=\frac{n}{2}(a_1+a_n) \\ \text{ Where: }a_1\text{ is the firm term \& }a_n\text{ is the last term} \end{gathered}[/tex]From the given question we have:
[tex]a_1=8,a_n=79,\text{ n =6}[/tex]Substitute these value in the expression of sum of n terms
[tex]\begin{gathered} S_n=\frac{n}{2}(a_1+a_n) \\ S_6=\frac{6}{2}(8+79) \\ S_6=3(87) \\ S_6=3\times87 \\ S_6=261 \end{gathered}[/tex]So, sum of 6 terms is 261
Write TWO facts about Pi
Solution:
Two facts about pi π
1) It is an irrational number.
2) It is ancient.
pls help this is due today and i have no idea what i am doing
(this isnt math but i didnt see music)
Why is it important for musicians to transcribe music?
Why do you think Beethoven’s story is unique (special)?
What are some ways that we can get better at active listening?
Below is a picture of a musical staff. What is a musical staff? What do the top lines and the bottom lines represent?
an image showing both staffs
What is a musical form? How does it make music more interesting?
Answer: look at explanation
Step-by-step explanation:
1. It helps you learn and listen to minor details in music better.
2. He had a handicap (partially deaf/deaf) but still managed to overcome and lay his mark in the music world.
3. Pay attention, eye contact, listen, pay attention to nonverbal cues, and show that you are listening
4. A foundation on which notes are drawn on. The lines represent a sound in music. A musical form is the structure of musical compositions. It makes music more interesting because it makes it organized and not jumbled up.
Only about 16% of all people can wiggle their ears. Is this percent different for millionaires? Of the 342 millionaires surveyed, 58 could wiggle their ears. What can be concluded at the α = 0.01 level of significance?For this study, we should use Select an answerThe null and alternative hypotheses would be: H0: ? Select an answer (please enter a decimal) H1: ? Select an answer (Please enter a decimal)The test statistic ? = (please show your answer to 3 decimal places.)The p-value = (Please show your answer to 3 decimal places.)The p-value is ? α Based on this, we should Select an answer the null hypothesis.Thus, the final conclusion is that ...The data suggest the population proportion is not significantly different from 16% at α = 0.01, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 16%.The data suggest the populaton proportion is significantly different from 16% at α = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 16%.The data suggest the population proportion is not significantly different from 16% at α = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is equal to 16%.Part a options:- a. t- test for a population mean- z-test for a population proportionPart b options:(left box): u; ?; p(right box): >; =; =/; >Part c options:t; zPart e options:<; >Part f options:ACCEPT, REJECT, FAIL
Part a:
In this study, we have only a reference value of 16% (the proportion of people that can wiggle ears) and a population of 342 millionaires whose results we want to compare with this reference value. Since there is a relativelly high number of millionaries that were surveyed, we should use the z-test for a population proportion.
Part b:
It p is the sample proportion, the null hypothesis, in this case, is given by:
[tex]H_0:p=0.16[/tex]Therefore, the alternative hypothesis is given by:
[tex]H_1:p\ne0.16[/tex]Part c:
According to the data, the z-score is given by:
[tex]z=\frac{\frac{58}{342}-\cdot0.16}{\sqrt{\frac{1}{342}\cdot\frac{58}{342}(1-\frac{58}{342})}}\approx0.473[/tex]Part d:
According to the normal table, the p-value related to z-score given by:
0.638
Part e:
Therefore, we can check that this p-value is > a
Part f:
Based on this, we should ACCEPT the null hypothesis.
Part g:
Thus, the final conclusion is that the data suggest the population proportion is not significantly different from 16% at a = 0.01, so there is statistially significant evidence to conclude that the population proportion of millionaries who can wiggle their ears is equal to 16%.
How do I solve this problem? To find the distance AB across a river, a distance BC=250 is laid off on one side of the river. It is found that B =119 degrees and C=27 degrees. Find AB
Given the following information, which is the best description of the data?Range—5, from 12 to 17Mode—14Median—14.5Mean—15The data is around 13.The data is around 12.The data is around 15.The data is around 17.
we have that
the best description of the data is
The data is around 15A gardening shop receives a shipment of 12 crates of plants. Each crate contains 18 plants. A worker displays all the plants on 24 shelves with the same number of plants on each shelf. How many plants are displayed on each shelf?
A. 6
B. 16
C. 9
D. 36
Thanks!
Answer:16
Step-by-step explanation:
Factor completely x^2+10x+21
Answer:
(x+3)(x+7)
Step-by-step explanation:
x2+10x+21
The middle number is 10 and the last number is 21.
Factoring means we want something like
(x+_)(x+_)
We need two numbers that
Add together to get 10
Multiply together to get 21
3 and 7:
3+7 = 10
3*7 = 21
Fill in the blanks in
(x+_)(x+_)
with 3 and 7 to get...
(x+3)(x+7)
Answer: (x+7)(x+3)
Step-by-step explanation:
We need to values that we will add and get 10 and two values we will multiply and get 21 which are 7 and 3
Sammy is a baker who wants to make profit on his baked goods if it fits him 3.20 or o make a dozen cupcakes how much should he sell them if he wants to make 35% profit
For there to be a profit,
[tex]\begin{gathered} \\ \text{profit}=\text{ selling price - cost price} \end{gathered}[/tex]From the question,
[tex]\begin{gathered} \text{Cost price = \$3.20} \\ \text{Percentage profit = 35\%} \end{gathered}[/tex]Concept: The formula for the percent profit is given below as
[tex]\text{percentage profit = }\frac{\text{profit}}{\cos t\text{ price}}\times100\text{ \%}[/tex]Select the conic section that represents the equation.3x² + 3y²-2x + 4 = 0
Given:
[tex]3x^2+3y^2-2x+4=0[/tex]First, we arrange the equation:
[tex]\begin{gathered} 3x^{2}+3y^{2}-2x+4=0 \\ 3x^2-2x+3y^2+4=0 \\ (3x^2-2x)+3y^2=-4 \end{gathered}[/tex]Further simplification of the given equation will give us a result with an imaginary number, making the equation a nonreal circle, or not a conic section.
17) A brand of coconut oil is updating its packaging. The old rectangular container was 1 foottall, 4 inches long and 2.5 inches wide, their new cylindrical container has a 4.5 centimeterradius and is 30 centimeters tall.a) Determine the volume of the rectangular container, 3 points(if needed round the final answer to the nearest hundredth.)b) Determine the volume of the cylindrical container. 3 points(if needed round the final answer to the nearest hundredth.)c) The company charges the same amount for each container. Is one of the containers abetter buy? Explain and show work that justifies your answer. 3 points
a) Volume of rectangular container:
1 foot = 12 inches
[tex]\begin{gathered} V=\text{tall}\times long\times wide \\ V=12\times4\times2.5 \\ V=120inches^3 \end{gathered}[/tex]b) Volume of the cylindrical container:
[tex]\begin{gathered} V=\pi\times r^2\times h \\ V=\pi\times(4.5)^2\times30 \\ V=\pi\times20.25\times30 \\ V=607.5\pi \\ V=607.5(3.14) \\ V=1907.55\operatorname{cm}^3 \end{gathered}[/tex]c) First, we convert the volumes of the containers into the same units.
For volume of the rectangular container in centimeters:
1 inch3 = 16.3871 cm3
[tex]V=120\times16.3871=1966.45\operatorname{cm}^3[/tex]With this, we can say that the rectangular container has a larger volume than the cylindrical container. Therefore, the cylindrical container is a better buy.
Answer:
a) V = 120 in^3
b) V = 1907.55 cm^3
c) Cylindrical container is a better buy
3/8 divided by 4/3.5
1) In this division, we need to turn that decimal number into a fraction:
[tex]undefined[/tex]State the number of possible real zeros and turning points of f(x) = x^7 – 6x^6 + 8x^5. Then determine all of the real zeros by factoring. 1) 7 real zeros and 6 turning points; 0, 2, and 42) 7 real zeros and 6 turning points; 0, –2, and –43) 6 real zeros and 5 turning points; 0, 2, and 44) 6 real zeros and 5 turning points; 0, –2, and –4
Step 1
The given equation is
[tex]f(x)=x^7-6x^6+8x^5[/tex]Required: To find the real zeroes by factorization and the turning points.
Step 2
Find the number of real zeroes
[tex]\begin{gathered} x^7-6x^6+8x^5=0 \\ x^5\mleft(x-2\mright)\mleft(x-4\mright)=0 \\ x^5=\text{ 0} \\ x\text{ = 0 five times} \\ ^{}or\text{ } \\ x-2\text{ = 0} \\ x=\text{ 2} \\ or \\ x-4=0 \\ x=\text{ 4} \\ \text{Therefore, there are 7 real zeroes} \end{gathered}[/tex]Step 3
Find the number of turning points.
[tex]f^{\prime}(x)\text{ = }7x^6-36x^5+40x^4[/tex][tex]\begin{gathered} As\text{ se}en\text{ from the differential, the number of turning points is found by subtracting 1 from the highest power of the function.} \\ \text{Hence, the number of turning points = 7-1 = 6} \\ \text{There are 6 turning points} \end{gathered}[/tex]Therefore, there are 7 real zeroes and 6 turning points; 0, 2 and 4
The answer is option A
Using P.E.M.D.A.S, how do I solve this?
Answer: 7
Step-by-step explanation:
First, do parenthesis- 2x4 is 8 and 8 times - is -8. Now it is 30/6+10-8. 30 divided by 6 is 5. 10-8 is 2. 5+2 is 7.
There are about 3.79 liters in 1 gallon. Kendra’s fish tank contains 100 gallons of salt water. About how many liters does the tank hold? Round your answer to the nearest whole number. Answer to get 60 points plus brainliest!
Answer:
379 liters
Step-by-step explanation:
3.79 L / gal * 100 gal = 379 Liters
Kendra's fish tank can hold 379 liters of water under the given conditions.
Given that,
There are about 3.79 liters in 1 gallon. Kendra’s fish tank contains 100 gallons of salt water.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
3.79 liters = 1 gallon,
Now,
in the fish tank
100 gallon of water = 3.79× 100 liters
= 379 liters
Thus, Kendra's fish tank can hold 379 liters of water under the given conditions.
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You go on a hayride to take photographs of landmarks. The map shows your path and two landmarks. Each unit in the coordinate plane corresponds to 10 yards. Approximate your minimum distance from the giant pumpkin. If necessary, round your answer to the nearest tenth.
Using the distance between a point and a line and the conversion of the units to yards, it is found that the minimum distance from the giant pumpkin is of 8.9 yards.
What is the distance between a points and a line?Suppose that we have a linear function defined according to the following rule, in standard notation:
Ax + By + C = 0.
And a point with coordinates given by:
P(x*,y*)
The shortest distance between the line and the point is given by:
[tex]d = \frac{|Ax^\ast + By^\ast + C|}{\sqrt{A^2 + B^2}}[/tex]
The line of the path in this problem has:
Intercept of 0, as when x = 0, y = 0.Slope of 0.5, as when x increases by 4, y increases by 2.Hence:
y = 0.5x.
-0.5x + y = 0
-x + 2y = 0.
The coefficients are:
A = -1, B = 2.
The giant pumpkin has coordinates given by:
(x*, y*) = (-4, -3).
Hence the distance in units is given by:
d = |(-1)(-4) + 2(-3)|/sqrt(5)
d = 2/sqrt(5)
d = 0.89 units.
Each unit is equivalent to 10 yards, hence the shortest distance in yards is given by:
0.89 x 10 = 8.9 yards.
What is the missing information?The problem is given by the image at the end of the answer.
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What is 4 square root of 4?
Answer:
8
Step-by-step explanation:
4[tex]\sqrt{4}[/tex]
The [tex]\sqrt{4}[/tex] is 2
4x2 = 8
Answer:The square root of 4 is simply just 2 or in other words, 4 = 2.
Step-by-step explanation:
The value of root 4 is equal to exactly 2. But the roots could be positive or negative or we can say there are always two roots for any given number.
Jacob is planting shrubs for a landscaping client. He planted more shrubs in the additional region so that the density of shrubs in the new region is equal to the density of shrubs in the rectangular region as shown.
ANSWER:
52 shrubs
STEP-BY-STEP EXPLANATION:
We know the number of trees planted in a given area, so to calculate the number of total trees, we must calculate the area of the entire figure and thus calculate by means of a proportion
We calculate the total area if we divide the figure in two, as follows:
The area of zone A, which is a rectangle, is calculated as follows:
[tex]\begin{gathered} A_A=b\cdot h \\ A_A=50\cdot20 \\ A_A=1000 \end{gathered}[/tex]The area of zone B, which is a triangle, is calculated as follows:
[tex]A_B=\frac{b\cdot h}{2}[/tex]To calculate the value of the height of the triangle, we apply the Pythagorean theorem on the right triangle that is formed:
Where the hypotenuse is 25 meters and the other leg is 15 meters, just like this:
[tex]\begin{gathered} h^2=a^2+b^2 \\ 25^2=15^2+b^2 \\ b=\sqrt[]{25^2-15^2} \\ b=\sqrt[]{400} \\ b=20 \\ \text{therefore the height is 20 meters, replacing:} \\ A_B=\frac{30\cdot20}{2} \\ A_B=300 \end{gathered}[/tex]Now, the total area would be the sum of both areas:
[tex]\begin{gathered} A_T=1000+300 \\ A_T=1300 \end{gathered}[/tex]Which means that if in an area of 400 square meters (20 * 20) they can plant 16 shrubs, in an area of 1300 square meters they would be:
[tex]\begin{gathered} \frac{16}{400}=\frac{x}{1300} \\ \text{ solving for x} \\ x=\frac{16\cdot1300}{400} \\ x=52 \end{gathered}[/tex]In other words, a total of 52 shrubs can be raised throughout the region.
Assuming the pattern continues, what is S12 for the series −5 − 14 − 23 − 32 − …?A)-104B)-624C)-654D)-663
The sum of the first 12 terms is s(12) = -624 if the sequence is series −5 − 14 − 23 − 32 option (B) is correct.
What is a sequence?
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
It is given that:
The sequence is:
−5 − 14 − 23 − 32 −
s(12) means the sum of the 12 terms
s(12) = (12/2)[-5 + (12-1)(-9)]
s(12) = 6[-5 -99]
s(12) = 6[-104]
s(12) = -624
Thus, the sum of the first 12 terms is s(12) = -624 if the sequence is series −5 − 14 − 23 − 32 option (B) is correct.
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7 John and Raul both bought the same style bike from a store. On
Wednesday, John purchased the bike at a 20% discount off the original
price. On Friday, Raul bought the bike for off the original price.
Part A-Who received the greater discount on the bike? Show your work.
Part B-If John saved $24, what was the original price of the bike? Show
your work.
Use words, numbers and/or pictures to show your work.
John recieved the greater discount and the original price of the bike is $120
John purchased the bike at a 20% discount off the original
price.
Let the price of the bike be x
The price at which John purchased the bike is x - 20% of x
= x - (20/100)x
=(80/100)x
Raul brought the bike at original price.
Raul's cost price is x
x is greater than (80/100)x
Raul purchased at a greater price than John, so the greater discount is recieved by John.
John got discount = (20/100) x
He saved = $24
(20/100)x = 24
20x =2400
x = 2400/20
x = 120
The original price is $120
Therefore, John recieved the greater discount and the original price of the bike is $120
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Mathew deposits 400800.00 kina with the bank which offers 5½% interest per annum. calculate the interest earned after four years if it is compounded annually?
Solution
For this case we can use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A= future value, P= present value= 400800.00
r= 5.5%=0.055, n =1 , t= 4 years
n= represent the number of times that the interest is compounded each year =1 for this case
Replacing we got:
[tex]A=400800\cdot(1+\frac{0.055}{1})^{4\cdot1}=496520.92[/tex]then we can find the interest in the following way:
[tex]I=A-P=496520.92-400800=95720.919[/tex]A student buys 5 books for $47.85. If all of the books are the same price, the cost of each book is
Answer: $9.57
Step-by-step explanation: 47.85/5 = 9.57. Therefore each book costs $9.57.
What is the equation of the line that contains the points ( -1 , 1 ) and ( 5 , -3) ?
ANSWER:
[tex]y=-\frac{2}{3}x+\frac{1}{3}[/tex]STEP-BY-STEP EXPLANATION:
The equation of the line in its slope and intercept form is as follows:
[tex]\begin{gathered} y=mx+b \\ \text{ where m is the slope and b is y-intercept} \end{gathered}[/tex]The slope can be calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing the points (-1 , 1) and (5 , -3) :
[tex]m=\frac{-3-1}{5-(-1)}=\frac{-4}{5+1}=-\frac{4}{6}=-\frac{2}{3}[/tex]Now, we calculate the value of b, with the help of the slope and the point (-1,1)
[tex]\begin{gathered} 1=-\frac{2}{3}\cdot-1+b \\ b=1-\frac{2}{3} \\ b=\frac{1}{3} \end{gathered}[/tex]Therefore, the equation would be:
[tex]y=-\frac{2}{3}x+\frac{1}{3}[/tex]
evaluate the expression 12x-3y when x is -1/4 and y is 3
Answer:
-12
Step-by-step explanation:
plug in and solve
1. 12(-1/4) - 3(3)
2. -12/4 - 9
3. -3 - 9
4. -12
The ratio of two cars, the Thunderbolt and the Flash, in terms of their miles per gallon was 6:5. The new version of the Flash added 14 miles per gallon and now the ratio is 24:27 .
What is the miles per gallon of the Thunderbolt?
The Thunderbolt gets
miles per gallon.
If the ratio the Thunderbolt and the Flash, in terms of their miles per gallon was 6:5 and the new version of the Flash added 14 miles per gallon and now the ratio is 24:27, then the miles per gallon of the Thunderbolt is 15.27 miles per gallon
The ratio the Thunderbolt and the Flash, in terms of their miles per gallon = 6:5
Then the miles per gallon of the Thunderbolt and the Flash is 6x and 5x respectively
The new version of the Flash added 14 miles per gallon
New ratio of the cars = 24:27
Therefore the equation is
5x+14 = 27x
27x-5x = 14
22x = 14
x = 7/11
The miles per gallon of the Thunderbolt = 24x
= 24×7/11
= 15.27 miles per gallon
Hence, If the ratio the Thunderbolt and the Flash, in terms of their miles per gallon was 6:5 and the new version of the Flash added 14 miles per gallon and now the ratio is 24:27, then the miles per gallon of the Thunderbolt is 15.27 miles per gallon
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Solve g(7) given g(X)= -3x+1
Step-by-step explanation:
that means we need to calculate the function result with x having a specific value.
for this we replace any appearance of x in the function expression by that specific value, and then we calculate.
g(x) = -3x + 1
g(7) means x = 7, and that gives us
-3×7 + 1 = -21 + 1 = -20
so, g(7) = -20
Answer:
-20
Step-by-step explanation:
Substitute 7 into the function g(x)
Since negatives "rule" positives,
7 * -3 = -21,
-21 + 1 = -20
Select the vector along which a translation of the plane would map point A to its image T(A).
The vector along which a translation of the plane would map point A to its image T(A) is: C. vector MN.
The types of transformation.In Geometry, there are different types of transformation and these include the following:
ReflectionDilationRotationTranslationWhat is a translation?A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.
In this context, we can reasonably infer and logically deduce that vector MN is a translation of the given plane which would map point A to its image point T(A) because they both move in the same direction.
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