Answers
Read my note at the end of problem 5 in another post.
You already know this table represents an exponential function
since each y-coordinate is always the previous y-coordinate multiplied by 6.
That means b = 6, and you have
y = a(6)^x
Now we find "a". When x = 0, y = 5. That means a = 5.
The equation is
y = 5(6)^x
Related Questions
A rectangular storage box is 12in. wide,15. long,and 9 in. high.how many square inches of colored paper are needed to cover the surface of the box?
Answers
(I had a question just like this)
What is (4a)^2 without exponents?
Answers
Please help. Web making by spiders is an example of which of the following
A. Innate behavior
B. Courtship
C.defensive behavior
D.reproducing
Answers
C. It's not defensive. It's meant to trap food. Spiders are carnivores and they eat what they catch. Webs are sticky and their pray can't get away.
A. Webs are constructed out of different types of silk, depending on what the web is for. The only thing you can eliminate is C. The silk itself is attractive to the opposite sex so courtship is a possibility. After the spider reproduces, the egg can be placed in a very dense covering of silk.
A is the all encompassing answer to the 11 things webs their silk are used for by spiders.
A <<<< answer.
A card is drawn from a well shuffled deck of 52 cards. find the probability of drawing a club or a diamond
Answers
[tex] |\Omega|=52\\
|A|=26\\\\
P(A)=\dfrac{26}{52}=\dfrac{1}{2}=50\% [/tex]
The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 5 cm/s. when the length is 14 cm and the width is 9 cm, how fast is the area of the rectangle increasing?
Answers
Differentiate with respect to time:
dA
----- = L*(dW/dt) + W*(dL/dt)
dt
Here,
dA
----- = (14 cm)*(5 cm/sec) + (9 cm)*(3 cm/sec)
dt
Finish the indicated multiplication and addition to obtain your final answer.
The area of the rectangle at L = 14 cm and B = 9 cm is increasing at 97 cm²/s.
What is the area of rectangle?
The area of a rectangle is given by -
A[R] = L x B
Given is the length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 5 cm/s.
Now, we can write -
dL/dt = 3 cm/s
dB/dt = 5 cm/s
We know, that the area is -
A = LB
differentiating both sides with respect to [t], we get -
dA/dt = L dB/dt + B dL/dt
dA/dt = 5L + 3B
At L = 14 cm and B = 9 cm.
(dA/dt) [14, 9] = 5 x 14 + 3 x 9 = 70 + 27 = 97 cm²/s
Therefore, the area of the rectangle at L = 14 cm and B = 9 cm is increasing at 97 cm²/s.
To solve more questions on application of derivatives, visit the link below-
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I need the answer I need help with this question
Answers
The origin is the midpoint between each vertex and its image.
Negate every coordinate value, for example, J(-5, -3) gets rotated to J'(5, 3).
What is the approximate difference in the growth rate of the two populations? The approximate difference in the growth rate is 10 percent. The approximate difference in the growth rate is 40 percent.
Answers
Answer:
B
Step-by-step explanation:
The approximate difference in the growth rate is 40 percent.
Two angels re supplementary. The larger angle is 48 degrees more than the 10 times the smaller angle. Find the measure of each angle.
Answers
STEP 1:
find the value of x
x= smaller angle
10x + 48= larger angle
Add the two angles above to equal 180.
x + (10x + 48)= 180
combine like terms
11x + 48= 180
subtract 48 from both sides
11x= 132
divide both sides by 11
x= 12° smaller angle
STEP 2:
find the value of the second angle
=10x + 48
=10(12) + 48
=120 + 48
=168° larger angle
CHECK:
12° + 168°= 180°
180°= 180°
ANSWER: The smaller angle is 12° and the larger angle is 168°.
Hope this helps! :)
The health care Jimmy’s employer offers is a fee-for-service plan in which Jimmy and his family must pay for $12,500 in health related services in a calendar year before the insurance company begins to pay. Jimmy and his family have several health related issues that demand $685.00 each month. If one of Jimmy’s children were to become seriously injured at the end of the year, how much more would Jimmy and his family need to pay before the insurance company begins to assume responsibility?
a.
$984.58
b.
$4,280.00
c.
$11,815.00
d.
$14,417.92
Answers
Total the amount they could incur because of health issues in a year then deduct it from 12,500.
= 685 x 12 months
= 8,220; they incur $8,220 for their health related issues in a year
= 12,500 - 8,220
= 4,280; amount they need to pay before the insurance company assumes responsibility.
The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square kilometers, find the dimensions of the rectangle.
Answers
2x - 6 = the width as given in the description.
Area of a rectangle is length * width. Now we plug in.
108 = x(2x - 6)
108 = 2x² - 6x
We are going to get all terms on the same side and factor.
2x² - 6x - 108 = 0
Factor out and divide each term by a GCF of 2 to get:
x² - 3x - 54 = 0
x² + 6x - 9x - 54 = 0
x(x + 6) - 9(x + 6) = 0
Your factors are (x + 6)(x - 9) = 0. Now we set each binomial equal to zero. This gives us x = - 6 and x = 9. Distance cannot be measure in negative numbers so we know to use x = 9 to find our measurements.
The length (x) is 9 kilometers. The width (2x - 6) is 12 kilometers when you plug in 9 where the x is.
The dimensions of the rectangle are [tex]\( \boxed{9 \text{ km} \times 12 \text{ km}} \)[/tex].
Let's denote the length of the rectangle as [tex]\( l \)[/tex] kilometers, and its width as [tex]\( w \)[/tex] kilometers.
From the problem statement, we have two pieces of information:
1. The width is 6 kilometers less than twice the length:
[tex]\[ w = 2l - 6 \][/tex]
2. The area of the rectangle is 108 square kilometers:
[tex]\[ lw = 108 \][/tex]
Now we can substitute the expression for \( w \) from the first equation into the second equation:
[tex]\[l(2l - 6) = 108\][/tex]
Expand and simplify the equation:
[tex]\[2l^2 - 6l = 108\][/tex]
Subtract 108 from both sides to set the equation to zero:
[tex]\[2l^2 - 6l - 108 = 0\][/tex]
Divide every term by 2 to simplify:
[tex]\[l^2 - 3l - 54 = 0\][/tex]
Now, we'll solve this quadratic equation using the quadratic formula, [tex]\( l = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex], where [tex]\( a = 1 \)[/tex], [tex]\( b = -3 \)[/tex], and [tex]\( c = -54 \)[/tex]:
[tex]\[l = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-54)}}{2 \cdot 1}\][/tex]
[tex]\[l = \frac{3 \pm \sqrt{9 + 216}}{2}\][/tex]
[tex]\[l = \frac{3 \pm \sqrt{225}}{2}\][/tex]
[tex]\[l = \frac{3 \pm 15}{2}\][/tex]
This gives us two possible solutions for [tex]\( l \)[/tex]:
[tex]\[l = \frac{18}{2} = 9 \quad \text{or} \quad l = \frac{-12}{2} = -6\][/tex]
Since length cannot be negative, we take [tex]\( l = 9 \)[/tex] kilometers.
Now, substitute [tex]\( l = 9 \)[/tex] back into the expression for [tex]\( w \)[/tex]:
[tex]\[w = 2l - 6 = 2 \cdot 9 - 6 = 18 - 6 = 12\][/tex]
Therefore, the dimensions of the rectangle are:
- Length [tex]\( l = 9 \)[/tex] kilometers
- Width [tex]\( w = 12 \)[/tex] kilometers
To verify, calculate the area:
[tex]\[l \times w = 9 \times 12 = 108 \text{ square kilometers}\][/tex]
Since this matches the given area, the dimensions [tex]\( l = 9 \)[/tex] kilometers and [tex]\( w = 12 \)[/tex] kilometers are correct.
Thus, the dimensions of the rectangle are [tex]\( \boxed{9 \text{ kilometers} \times 12 \text{ kilometers}} \)[/tex].
what is the quotient of 15p^-4q^-6/-20^12q^-3 in simplified form
Answers
[tex] \frac{15p^{-4} }{-20^{12} q^{3} } [/tex]
Determine the sign of the fraction.
[tex] -\frac{15p^{-4} }{20^{12} q^{3} } [/tex]
Now if a negative exponent is in the numerator,, then you must move the expression to the denominator and then make the exponent positive. This will change the expression to the following:
[tex]- \frac{15}{ 20^{12} q^{3} p^{4} } [/tex]
Lastly,, use the commutative property to reorder the terms on the bottom of the fraction.
[tex]- \frac{15}{ 20^{12} p^{4} q^{3} } [/tex]
Since we cannot simplify this expression any further,, the correct answer to this question is [tex]- \frac{15}{ 20^{12} p^{4} q^{3} } [/tex].
Let me know if you have any further questions.
:)
The simplified form of the expression: [tex]\( -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^3} \)[/tex]
To simplify the expression [tex]\( \frac{15p^{-4}q^{-6}}{-20^{12}q^{-3}} \)[/tex], we can apply the rules of exponents and simplify each part of the expression separately.
First, let's rewrite [tex]\( -20^{12} \) as \( -(20^{12}) \)[/tex] to make it clear that the exponent applies to the entire term:
[tex]\[ \frac{15p^{-4}q^{-6}}{-(20^{12}q^{-3})} \][/tex]
Now, let's simplify each part:
1. \( p^{-4} \) can be rewritten as [tex]\( \frac{1}{p^4} \).[/tex]
2. \( q^{-6} \) can be rewritten as [tex]\( \frac{1}{q^6} \).[/tex]
3. [tex]\( 20^{12} \)[/tex] can be calculated.
[tex]\[ \frac{15}{-(20^{12})} \times \frac{1}{p^4} \times \frac{1}{q^6} \times \frac{1}{q^{-3}} \][/tex]
Now, let's calculate [tex]\( 20^{12} \):[/tex]
[tex]\[ 20^{12} = (2^2 \times 5)^{12} = 2^{24} \times 5^{12} \][/tex]
[tex]\[ = (2^4)^6 \times 5^{12} = 2^{24} \times 5^{12} \][/tex]
Now, we can rewrite the expression:
[tex]\[ \frac{15}{-(2^{24} \times 5^{12})} \times \frac{1}{p^4} \times \frac{1}{q^6} \times \frac{1}{q^{-3}} \][/tex]
[tex]\[ = -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^6 \times q^{-3}} \][/tex]
[tex]\[ = -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^3} \][/tex]
This is the simplified form of the expression.
HELP ME PLS BBRAINLIESST AND 10 POINTS
Answers
Look on the row for "not like pink". Your probability is the number under "not like black" divided by the total for "not like pink".
A string of christmas tree lights has 15 lights what is the probability that the defective light is the 3rd from the plug
Answers
1.)Simplify the expression: 4 times Start Root 18 End Root plus 5 times Start Root 32 End Root
2.)Simplify the expression: 7 times Start Root 5 End Root minus 3 times Start Root 80 End Root
3.)Simplify the expression: Start Root 21 End Root times Left Parenthesis Start Root 3 End Root plus Start Root 14 End Root Right Parenthesis.
4.)Simplify by rationalizing the denominator: Start Fraction 4 over Start Root 10 End Root minus Start Root 6 End Root End Fraction
I WILL MAKE YOU THE BRAINIEST! PLEASE HELP
Answers
2.) -5 start root 5 end root
3.) 3 start root 7 end root + 7 start root 6 end root
4.) start root 10 end root + start root 6 end root
hope this helped :)
Answer:
I agree with Sydneyjones :D i very much agree
1.) 32 start root 2 end root
2.) -5 start root 5 end root
3.) 3 start root 7 end root + 7 start root 6 end root
4.) start root 10 end root + start root 6 end root
need help for question one in polynomials
Answers
Answer:
a) monomial
b) constant
c) binomial
d) trinomial
e) binomial
f) constant
g) monomial
Step-by-step explanation:
Let's start by defining the terms in the question:
A monomial is an expression with a single term, regardless of how many variables are in the term.
A binomial is an expression with two different terms, which cannot be combined into a single term due to their variables not matching.
A trinomial is an expression with three different terms, which cannot be combined into a binomial or monomial because their variables do not match.
A constant is an integer that lacks a variable attached to it. An integer with a variable attached to it would be a monomial, and the integer itself would be called a coefficient.
Now, we can get into the parts of the question:
a) 8a²b is two variables however it is still a single term so this is a monomial.
b) -39 is an integer with no variables attached. Therefore, it is a constant.
c) x + y is two variables and two different terms that cannot be combined into one single term. It is a binomial.
d) -12xy + 5y - x² showcases three different variables and three different terms that cannot be consolidated. Thus, it is a trinomial.
e) 2x² + 2y² demonstrates two different variables and two different terms that are not alike. As such, we have a binomial.
f) 3/4 is an integer with no variables in sight. We have here a constant.
g) -32m²n² has two variables but is only a single term on its own. This is a monomial.
A 12.0-cm segment makes a 108.0-degree angle with a 16.0-cm segment. To the nearest tenth of a cm, find the third side of the triangle determined by this SAS information.
Answers
Begin by using the cosine rule to find the unknown side.
Where a- unknown side, b is 12, c is 16 and angle in between is 108°
The cosine rule...
a² = b² + c² - 2bc cosA
= 12² + 16² - (2×12×16 cos108°)
= 518.655076
Taking the positive square root...
a = 22.774
a = 22.8 cm nearest tenth
The question involves finding the length of the third side of a triangle using the Law of Cosines. The known parameters are two sides and the included angle. The formula c² = (12 cm)² + (16 cm)² - 2*(12 cm)*(16 cm)*cos(108 degrees) can be used to calculate the length of third side.
Explanation:In this problem, you're dealing with a triangle and need to find the length of the third side. This is a classic case of using the Law of Cosines - a geometric rule that helps you find the length of a side of a triangle when you know the lengths of the other two sides and the angle in between (or in this case, SAS information).
The Law of Cosines formula is: c² = a² + b² - 2ab*cos(C), in which 'a' and 'b' represent the sides of the triangle adjacent to angle 'C', and 'c' is the other side. In your case, 'a' is 12.0 cm, 'b' is 16.0 cm and angle 'C' is 108.0 degrees. The third side 'c' can be calculated accordingly.
So, in this scenario, c² = (12 cm)² + (16 cm)² - 2*(12 cm)*(16 cm)*cos(108 degrees). With some basic arithmetic and the use of a calculator to compute the cosine, you can determine the length of the third side, 'c', to the nearest tenth of a cm.
Learn more about Law of Cosines here:https://brainly.com/question/21634338
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Maria is playing a game where she is trying to draw a spade from a standard deck of cards. if she doesn't get a spade, she replaces the card, shuffles the deck, and tries again. if she draws a card 3 times and doesn't get a spade, she loses. what is the probability that maria loses the game?
A.17.8%
B.23.7%
C.42.2%
D.31.6%
Answers
Answer:
The correct answer is C. 42.2%
Step-by-step explanation:
Total number of cards in the deck of playing cards = 52
Number of spades in the deck of playing cards = 13
Number of cards other than spade = 52 - 13
= 39
If she draws a card 3 times and doesn't get a spade, she loses.
So, She loses only if he gets all the three cards other than spade
[tex]\text{Probability that she does not get a spade in first draw = }\frac{39}{52}[/tex]
Now, The card is replaced if she does not get a spade.
[tex]\text{So, Probability that she does not get a spade in second draw = }\frac{39}{52}[/tex]
[tex]\text{Similarly, Probability that she does not get a spade in third draw = }\frac{39}{52}[/tex]
[tex]\text{Thus, Probability that she will lose the game = }\frac{39^3}{52^3}=0.422[/tex]
[tex]\text{Also, The percentage of Probability that she will lose the game = }0.422\times 100=42.2\%[/tex]
Hence, The correct answer is C. 42.2%
The cost function for kara's new clothing store where she sells t-shirts is c = $9.90n + 1060. what is the slope of the cost function for kara's new store?
Answers
In our cost function [tex]c=9.90n+1060[/tex], [tex]y=c[/tex] and [tex]x=n[/tex], so we can infer that the independent variable is [tex]n[/tex]. Since the coefficient of [tex]n[/tex] is 9.90, the slope of the cost function is 9.90.
We can conclude that the slope of Kara's new store cost function is $9.90
Answer:
The slope of the function is 9.90
Step-by-step explanation:
You can find the slope by looking at the coefficient of the independent variable in the equation. In this case, we would be looking for the coefficient of n.
Any help I don’t really understand this
Answers
The point is how to remove the brackets when a minus sign is on the left hand side. A second problem is how to get all the terms on one side over to the other.
Step One
Remove the brackets on the left side. This is an absolutely necessary step in the rest of your mathematical studies. What was done in this step affects all three terms on the inside of the brackets. Minus signs are real bad things to misuse. Study carefully how to change the signs when multiplying by a minus.
Rule a minus sign outside the brackets, when multiplied by anything inside the brackets, change the sign to the opposite of what it was.
-20 + 4x + 5x^2 = 20 - 7x^2
Comment
Before doing the last step, look at the answers. Two of them are 40. That is the answer for 20 and -20 when transferred. It's 40 which is a plus. So you should be transferring from left to right.
Step Two
Transfer from left to right.
-20 + 4x + 5x^2 = 20 - 7x^2 Add 20 to both sides.
4x + 5x^2 = 20 + 20 - 7x^2 Subtract 4x from both sides.
5x^2 = 40 - 7x^2 - 4x Subtract 5x^2 from both sides
0 = 40 - 7x^2 - 5x^2 - 4x
0 = 40 - 12x^2 - 4x Now you have to put them in the right order.
0 = 40 - 4x - 12x^2 <<<<< Answer
In bridge each player is dealt a hand of 13 cards from a deck of 52 cards. there are 4 aces in the entire deck. what are the expected number of aces in a single hand of cards?
Answers
Expected number of aces in a single hand of cards = 1/13 x 13 = 1
Answer: 1 ace card
List the following stocks and bonds in order from lowest default risk to highest default risk:
Bond in a stable foreign government
Preferred stock
Common stock
A. foreign government bond, common stock, preferred stock
B. foreign government bond, preferred stock, common stock
C. common stock, preferred stock, foreign government bond
D. preferred stock, common stock, foreign government bond
Answers
Common and preferred stock both represent the ownership of a corporation, but preferred stockholders are paid before common stockholders, both in good and bad times.
Therefore, from least to highest default risk we have a bond in a stable foreign government, preferred stock and then, common stock.
Hence, the correct answer is B. foreign government bond, preferred stock, common stock.
Marilyn uses a credit card with a 19.9% APR compounded monthly to pay for car repairs totaling $991.38. She can pay $410 per month on the card. What will the total cost of this purchase be?
$1,021.01
$1,188.66
$991.38
$1,192.39
Answers
$991.38 × 0.199/12 = $16.44
The balance subject to the next month's finance charge will be
$991.38 +16.44 -410.00 = $597.82
The finance charge at the end of the second month will be
$597.82 × 0.199/12 = $9.91
The balance remaining after the second payment will be
$597.82 +9.91 -410.00 = $197.73
The finance charge applied at the end of the third month is
$197.73 × .199/12 = $3.28
so Marilyn can make one final payment of
$197.73 +3.28 = $201.01
to pay off the balance.
In all, Marilyn has paid 2×$410.00 +201.01 =
$1021.01 . . . . . . . . corresponds to the first choice
_____
In real life, Marilyn's credit card may not accrue any finance charge until after the first statement on which the charge appears. Thus the total cost of the purchase may be only $1004.02. The attached spreadsheet shows the beginning balance and the finance charges for each month for the two different scenarios.
Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2?
A) 3x2 − 11x + 8 may or may not be a polynomial
B) 3x2 − 11x + 8 will be a polynomial
C) 3x2 − x + 4 may or may not be a polynomial
D) 3x2 − x + 4 will be a polynomial
Tip: Every 2 after 3x is an exponent.. so it would be 3x^2
Answers
3x^2 - 6x + 2 will be a polynomial
======================================
Explanation:
Line up the terms and subtract straight down
3x^2 - 6x + 2
5x - 6
-----------------
3x^2 -11x + 8
this is a polynomial as it is a sum of three monomials
Subtraction of any two polynomials will result in another polynomial. This is what closure means. In math terms, closure is the idea of taking two objects and performing some operation on them (eg subtraction). If we get the same type of object back, then the set of considered closed under that operation.
Here's another example of closure. Take two glasses of water and pour them together. The two glasses can be of different shapes and sizes. It doesn't matter. The fact that we have two containers of water is all that matters. In this example,the water is like the polynomial. Combining the two containers of water into one will result in a greater amount of water. Combining water with water leads to more water.
Jordan travels 3/4 of a mile longer to school each day than harisson does. combined, they have traveled 5 1/4 miles to school. how far does each trave;?
Answers
let harissom travel Y mile
given
X=Y plus 3/4 of y =1.75Y (3/4=0.75)
X+Y = 5.25(1/4=0.25)
now we can just put thevalue of X and we get
X+Y=5.25
1.75Y + Y= 5.25
Y=1.909
x= 1.75 × 1.909= 3.341
HELP, MARKING BRAINLIEST
How many compass settings are required to complete the construction?
Answers
Hint: if you don't know the answer you can count the number of arcs
The tree diagram shows Pam’s choices for her appetizer and a meal at a restaurant. How many choices include chicken
Answers
Answer is 8, i just did it
How do you solve this problem?
Answers
Step One
Find AB, BC, AC
Before beginning this problem, I'm going to arbitrarily name
c = AB
a = BC
b = AC It just makes the calculations easier.
AB = radius of the large circle - radius of the medium circle = 20.62 - 8.04 = 12.58
BC = Radii of the two smaller circles added together = 8.04 + 7.35 = 15.39
AC = Radius of the large circle - Radius of the small circle = 20.62 - 7.35 = 13.27
So
a = 15.39
b = 13.27
c = 12.58
Step Two
Find Angle A or <BAC
a^2 = b^2 + c^2 - 2*b*c * Cos(A)
15.39^2 = 12.58^2 + 13.27^2 - 2 * 12.58 * 13.27 * Cos(A)
236.852 = 158.26 + 176.1 - 333.87 * Cos(A)
236.852 = 334.4 - 333.87*Cos(A)
-97.55 = - 333.87 * Cos(A)
-97.55 / -333.87 = Cos(A)
0.2922 = cos(A)
A = cos-1(0.2922)
A = 73.01 degrees
Step Three
Just to see if you understand what was done, I'll give you the givens for finding c, and the answer and you can work through the calculations to see if your answer agrees with mine. If it doesn't PM me.
c = 12.58
b = 13.27
a = 15.39
12.58^2 = 13.27^2 + 15.39^2 - 2*13.27*15.39*Cos(C)
C = 51.42
Step Four
Find <B
Every triangle has 180 degrees so
B = 180 - <A - C
B = 180 - 51.42 - 74.01
B = <54.57.
I have found a moderator who opened the question up so that I can show you why the Cos law is the only way to do this. If the circles are very disproportionate as in this diagram, then no simple assumption can be made. The cos law is all that will work. I would have posted this earlier, but I didn't think anyone would find another method. It's ingenious but not possible for the situation below.
I would appreciate it if someone could take a look at my work on this calculus question and let me know if my work is correct!
Answers
_____
The second blue line in part A should identify the point on the curve as (-1, 1).
You can stop at any point in the development of the equation for a line, as the problem only asks for "an equation", not one in any specific form.
One hose can fill a pool in 12 hours. another hose can fill the same pool in 8 h
Answers
Explanation:
One hose can fill a pool in 12 hours.
The other house can fill the same pool in 8 hours.
If they fill the pool together,
[tex]\text {Time Needed } = \cfrac{12 \times 8}{12 + 8} = 4.8 hours [/tex]
What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?
Answers
-12 + 20x >= -6x + 9
-12+20x>-6x+9
-12+26x>9
26x>21
Now divide both sides by 26, and the answer is:
Answer: x is greater than or equal to 21/26 (21 over 26)