Answer:
[tex]C. \[/tex] [tex]\frac{1}{2}x^3 + 3.4y = 21[/tex]
Step-by-step explanation:
Given
[tex]x = 2[/tex]
[tex]y = 5[/tex]
Required
[tex]\frac{1}{2}x^3 + 3.4y[/tex]
Substitute 2 for x and 5 for y;
The expression becomes
[tex]=\ \frac{1}{2} * 2^3 + 3.4 * 5[/tex]
Multiply 3.4 by 5
[tex]=\ \frac{1}{2} * 2^3 + 17[/tex]
---------------------------
[tex]2^3 = 2 * 2 * 2 = 8[/tex]
--------------------------
[tex]=\ \frac{1}{2} * 8 + 17[/tex]
[tex]=\ \frac{8}{2} + 17[/tex]
[tex]=\ 4 + 17[/tex]
[tex]=\ 21[/tex]
Hence;
[tex]\frac{1}{2}x^3 + 3.4y = 21[/tex]
A doctor prescribes 500 milligrams of a therapeutic drug that decays by about 19% each hour.
a) To the nearest minute, what is the half-life of the drug?
b)
Write an exponential model representing the amount of the drug remaining in the patient's
system after t hours. (2 points)
c)
Use your formula to find the amount of drug that would remain in the patient's system after 24
hours. Round your answer to the nearest hundredth of a gram. (2 points)
Answer:
a) half life is 3h 17 minutes
b) function of residue drug after t hours with initial quantity = 500 mg
f(t) = 500 (0.81^t)
c) drug left in patient's system after 24 hours
= 0.00 grams (to the hundredth of a gram.
Step-by-step explanation:
Given:
Drug initial active weight, A = 500 mg
Residue active weight, f(t) = A 0.81^t
t = time in hours.
a) half life
Half life is T, such that f(T) = 0.5A =>
0.5A = A(0.81^t)
0.81^t = 0.5
t*log(0.81) = log(0.5)
t = log(0.5) / log(0.81) = -0.6931 / -0.2107 = 3.2894 hours
= 3 h 17.36 minutes
b) Equation of function of residue drug as a function of time t in hours
A=500 mg
f(t) = A(0.81^t) substitute A = 500 mg
= 500(0.81^t) mg
c) weight of residue drug after 24 hours to the hundredth of a gram.
t=24 hours
A=500
f(t) = 500(0.81^t) substitute t=24 hours
= 500(0.81^24)
= 3.181 mg
= 0.003181 g
HELP A GIRLL OUT I GAVE YOU ALL MY POINTS!! HELPP! 1. a. What is James’s new texting speed if he practices for only 1 month? __________ b. What is James’s new texting speed if he practices for 2 months? ____________ c. What is his new texting speed if he practices for 3 months? _____________ 2. Write an algebraic equation that gives James’s texting speed s for m months of practice. 3. solve the equation from question 2 to determine how many months of practice it will take before james texting speed reaches 8 characters per second. Lynda would also like to complete in the same speed texting completion as james she currently texts at the rate of 4 characters per second but will only have 10 months to practice before the completion. 4. if Lynda wants to text at least 8 characters per second like james then the equation 10r+4=8 could be used to model this situation. Solve for r. 5. Explain what the variable r represents in the equation given in question 4. 6. Consider the equation 8x+5=37 write a real life scenario that this equation could model.
Answer:
1. a. His new texting speed after one month is 2 + 1/2 = 2.5 characters per second.
b. After two months it will be 2 + (1/2) * 2 = 3 characters / second.
c. Answer is 2 + 1/2 * 3 = 3.5 characters/second/.
2. The answer is s = 1/2m + 2
3. To solve for m we write 8 = 1/2m + 2 → 6 = 1/2m → m = 12 months.
4. 10r + 4 = 8 → 10r = 4 → r = 0.4
5. The variable r represents the rate she must increase her texting speed by per month.
6. A scenario could be "Allison has 37 marbles in a jar. She took out 5 from the jar and wants to divide the remaining amount equally among her 8 friends. How many marbles does each friend get?".
Determine the measure of obtuse angle A. answers: A) 130° B) 122° C) 58° D) 7°
Answer:
B) 122 degrees.
Step-by-step explanation:
Consider the kite :- the 2 angles at the tangents are 90 degrees so we have:
9x - 5 + 14x + 24 + 90 + 90 = 360
9x - 5 + 14x + 24 = 180
23x + 19 = 180
23x = 161
x = 7
So the obtuse angle = 14(7) + 24
= 98 + 24
= 122 degrees.
URGENT!!! Please answer ASAP with full working out thank you
Step-by-step explanation:
[tex]a)
\\ \frac{a}{x - 1} - \frac{2}{x + 1} = \frac{4}{(x - 1)(x + 1)} \\ \\ \frac{a(x + 1) - 2(x - 1)}{(x - 1)(x + 1)} = \frac{4}{(x - 1)(x + 1)} \\ \\ a(x + 1) - 2x + 2 = 4 \\ \\ a(x + 1) = 4 + 2x - 2 \\ \\ a(x + 1) = 2x + 2 \\ \\ a (x + 1) = 2(x + 1) \\ \\ a= \frac{2(x + 1)}{(x + 1)} \\ \\ \huge \red{ \boxed{a = 2}}[/tex]
Solve b part yourself in the same way.
The expression 14s(s - 1) can be used to find
the total number of cards created by the ninth
grade students. Based on the given information,
which of the following statements must be true?
Select all that apply.
Answer:
B. The variable s represents the number of students in each class.
C. The coefficient 14 represents the number of classes in the 9th grade.
Step-by-step explanation:
The total number can be found by multiplying the number of the things with the number of people producing it. For example if 5 boys make 5 colored ropes the total number of ropes will be 5*5= 25.
In this question the combinations rule is used for variuos number of classes which are 14. Now we have to find the number of students which are s (s-1). Suppose s= 6 so the number of students would be 6(6-1) = 6(5) = 30
We will multiply the number of classes 14 with the number of students s(s-1) to get the total number of cards produced.
Which graph represents the solution set for the system x + y> 5 and -3x + 2y< -2.
The sum of two numbers is 88; one number is 12 less than the other. What is the larger number? 1. Cut the _______ number in half. Write both halves on your paper. 2. Cut the ______________in half. 3. Now ADD half and SUBTRACT half from each side.
Answer:
50
Step-by-step explanation:
I have set up an equation, where 'x' is the larger number:
x + (x - 12) = 88
Solve for 'x':
x + (x - 12) = 88
x + x - 12 = 88
2x - 12 = 88
2x -12 + 12 = 88 + 12
2x = 100
2x/2 = 100/2
x = 50
The larger number should be 50.
Answer:50
Step-by-step explanation:
-
Given the graph of y = f(x), shown as a red dashed curve, drag the movable blue point to obtain the graph of
y = f(x - 4) + 3.
Answer:
The blue point will be at (4, 3)
Step-by-step explanation:
Numbers inside the parenthases only affect x, but are revered. If it is -4, move right 4. lf it is 4, move left 4.
Numbers after the patentheses affect the movement of y. When the point is at (4, 0), move up 3.
What are all of the real roots of the following polynomial? f(x) = x4 - x3 - 13x2 + x + 12
We can find roots by setting f(x) = 0 --> x^4 - x^3 - 13x^2 + x + 12 = 0.
Factoring f(x) to make things easier for us gives us (x - 1)(x + 1)(x - 4)(x + 3), which, equal to 0, gives us the ability to set each set of parentheses = 0.
x - 1 = 0 gives us x = 1.
x + 1 = 0 --> x = -1.
x - 4 = 0 --> x = 4.
x + 3 = 0 --> x = -3.
our roots are x = 1, -1, 4, and -3.
*ANSWER ASAP PLS* Lucy is covering a box with fabric for a craft festival. If the box is an 8-inch cube, how much fabric does she need? a.)252 sq.in. b.)384 sq.in. c.)240 sq.in.
Answer: b) 384 sq. in.
Step-by-step explanation:
Surface area of cube = 6a^2
= 6 (8)^2
= 6 x 64
= 384 sq. in.
How did the temperature change if: at first it decreased by 10 % and then decreased by 30% ?
Answer:
We decreased by 37%
Step-by-step explanation:
Let x be the starting temperature
We decrease by 10 percent which means we are left with 100-10 =90 percent
.90 x
Then we decrease by 30 percent, 100 - 30 = 70
( .90x) * .70
.63x
We have .63 of the original left or 63%
100 -63 = 37
We decreased by 37%
Answer:
37% and it decreased
Step-by-step explanation:
Need Help Please I'm Out Of Time ;(
Which of the following questions are statistical questions? Select all that apply
How far does Mary live from school?
How many students were absent from Mrs. Jenssen's class today?
How tall are the sixth-grade students in your school?
How many pull-ups can each student in your class do?
What was the temperature at 4 p.m. each day this week?
Answer:
last three questions are statistical question
Answer:
The last three questions
Step-by-step explanation:
HELP!!! How far have I travelled if I biked at 10mph for hhrs, I walked at 3mph for twice as long as I biked, and ran at 10mph for one quarter as long as I walked?
Answer:
21h miles
Step-by-step explanation:
The appropriate relation is ...
distance = speed · time
__
We are given that ...
biking time = h
walking time = 2h
running time = (1/4)(2h) = h/2
The total distance traveled is ...
total distance = biking distance + walking distance + running distance
= (10)(h) +(3)(2h) +(10)(h/2)
= 10h + 6h + 5h
total distance = 21h . . . miles
Answer:
21h miles
Step-by-step explanation:
The appropriate relation is ...
distance = speed · time
__
We are given that ...
biking time = h
walking time = 2h
running time = (1/4)(2h) = h/2
The total distance traveled is ...
total distance = biking distance + walking distance + running distance
= (10)(h) +(3)(2h) +(10)(h/2)
= 10h + 6h + 5h
total distance = 21h . . . miles:
A trader claims that the proportion of stocks that offer dividends is different from 0.14. If the trader wants to conduct a hypothesis test, should they use a left-, right-, or two-tailed hypothesis test to analyze whether the proportion of stocks that offer dividends is different from 0.14? Select the correct answer below: Left-tailed test Right-tailed test Two-tailed test
Answer:
The correct option is;
Two-tailed test
Step-by-step explanation:
From the interpretation of the question statement, the trader wants to conduct a hypothesis test on the trader's claim that the proportion of stocks that offer dividends is different from 0.14
Given that the difference is hypothesized, then the null hypothesis, H₀ and the alternative hypothesis, H₁ should be written as follows;
H₀: Null hypothesis (no difference, or no change)
H₁: μ ≠ μ₀ which is hypothesizing difference which is known as a two-tailed test
The confidence level is then selected and the test statistic is calculated
10) Spike drives for 50 miles at 60mph. He slows down and travels
another 50 miles at 40mph. For the final part of the 120 mile journey,
he speeds up to 80mph. How long does he take altogether? What is
his average speed (to the nearest mph)?
Answer:
2 1/3 hours or 2 hours 20 minutes.
51.4 mph to 1 decimal place.
Step-by-step explanation:
Time = distance speed
First 50 miles time taken = 50 / 60 = 5/6 hours
Second 50 miles - time = 50/40 = 5/4 hours.
Final 20 miles - time taken = 20 / 80 = 1/4 hours.
Total time taken = 5/6 + 5/4 + 1/4
= 5/6 + 6/4
= 10/12 + 18/12
= 28/12
= 7/3 or 2 1/3 hours or 2 hours 20 minutes.
Average speed = total distance / total time
= 120 / 7/3
= 120 * 3/7
= 51.4 mph to 1 decimal place.
Please help solve i give brainliest
Answer:
(0,3)
Step-by-step explanation:
y = 2x+3
y = -3x+3
Since both equations are equal to y, set them equal to each other
2x+3 = -3x+3
Subtract 3 from each side
2x = -3x
Add 3x to each sdie
2x+3x = -3x+3x
5x =0
Divide by 5
x=0
Now solve for y
y =2x+3
y = 0+3
y=3
(0,3)
Answer:
(0,3)
Step-by-step explanation:
y = 2x+3
y = -3x+3
2x+3 = -3x+3
2x = -3x
2x+3x = -3x+3x
5x =0
x=0
The solve for y
y =2x+3
y = 0+3
y=3
(x,y)=(0,3)
Then (0,3) will be your answer!
Hope this help!
If a sample consists of the following data values, what is the sample mean?
13, 91, 44, 68, 54, 16, 88, 74
Answer:
mean =sum of all data values
total number of data
13+91+44+68+54+16+88+74
8
448
8
=56
therefore the mean is 56
Answer: 51
Step-by-step explanation:
Determine the surface area of a sphere with a diameter of 16 cm. Question 4 options: A) 804.2 cm2 B) 1,024 cm2 C) 201.0 cm2 D) 3,216.9 cm2
Answer:
The answer is option A.
804.2cm²Step-by-step explanation:
Surface area of a sphere is 4πr²
where r is the radius
radius = diameter / 2
radius = 16/2 = 8cm
Surface area of the sphere is
4π (8)²
= 4(64)π
= 256π
= 804.2cm²
Hope this helps you.
Fill in the blank with a number to make the expression a perfect square.
Answer:
16
Step-by-step explanation:
[tex] {w}^{2} - 8w + { {4}^{2} } \\ = {w}^{2} - 8w + \boxed{ 16} \\= (w-4)^2 [/tex]
Answer:
Step-by-step explanation:
a² + 2ab +b² = (a+ b)²
w² - 8w + _?___
a = w
2ab = -8w
2*w*b = -8w
b = -8w/2w
b = 4
8w = 2 * 4*w
w² - 8w + 4² =w² -8w + 16
310
Which law would you use to simplify the expression
quotient of powers
power of a quotient
product of powers
power of a product
power of a quotient
edge 2021
The law used to simplify the expression is quotient of powers.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, 3¹⁰ / 3⁴, we need to determine the law used to simply the expression,
3¹⁰ / 3⁴
For this case we have an expression formed by a division of powers of the same base in which we must apply a law to simplify said expression.
By the definition we have the property of the power quotient of the same base set:
xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾
So, using the same,
3¹⁰ / 3⁴ = 3⁽¹⁰⁻⁴⁾ = 3⁶
Thus, to simplify the expression we must use the property of the power quotient of the same base.
Hence, the law used to simplify the expression is quotient of powers.
Learn more about expression, click;
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P(A) = .20 P(B) = .25 P(A and B) = .10 What is P(B given A)
P(B given A) = P(A and B) / P(A)
P(B given A) = 0.10 / 0.20
P(B given A) = 0.50
Which of the following is not a condition that must be met before you can use
the quadratic formula to find the solutions of an equation?
Answer:
D. The coefficient of the x^2-term must be positive.
Step-by-step explanation:
A. The coefficient of the x2-term can't be zero.
B. There can be no term whose degree is higher than 2.
C. One side of the equation must be zero.
D. The coefficient of the x2-term must be positive.
Quadratic equation is given as:
y=ax^2+bx+c
To use the quadratic formula,we have
ax^2+by+c=0
Coefficient of x^2 can not be equal to 0, that is a can not be equal to 0
There can be no term whose degree is higher than 2. The highest degree in a quadratic equation is 2
One side of the equation must be 0, that is ax^2+by+c=0
Coefficient of x^2 must be positive. The coefficient of x^2 can either be positive or negative. That is, it can either be a or -a
steve can run 3.5 miles in 30 minutes. if he increases his rate by 1/2 mile per hour, how far will he run in 2 hours?
Answer:
15 miles
Step-by-step explanation:
Currently, he can run 3.5 * 2 = 7 mph. Adding 1/2 mph to that gives us 7.5 mph, so therefore, in 2 hours he can run 7.5 * 2 = 15 miles.
Answer:
15
Step-by-step explanation:
because its correct just did the thing.
I NEED HELP ASAP!!!!! WILL MARK BRAINLIEST!!!!!!
Answer: 16
Step-by-step explanation:
The 7 and the 9.
Look closely
Which letter comes next? F H K N Z ? Choose from: L M T Y
Answer:
t
Step-by-step explanation:
The letter that comes next in the given sequence is K.
The given sequence is F H K N Z.
We need to find which letter comes next in the given sequence.
What is the pattern followed in the given sequence?The pattern followed by the given sequence is they are letters of sounding board consonants.
Therefore, the letter that comes next in the given sequence is K.
To learn more about the sequence visit:
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6d-\dfrac{11}2=2d-\dfrac{13}26d− 2 11 =2d− 2 13
Answer:
So your answer is d = -1/4 = -0.250
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
6*d-11/2-(2*d-13/2)=0
13
Simplify ——
2
11 13
(6d - ——) - (2d - ——) = 0
2 2
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
2d 2d • 2
2d = —— = ——————
1 2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2d • 2 - (13) 4d - 13
————————————— = ———————
2 2
11 (4d - 13)
(6d - ——) - ————————— = 0
2 2
11
Simplify ——
2
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
6d 6d • 2
6d = —— = ——————
1 2
4.2 Adding up the two equivalent fractions
6d • 2 - (11) 12d - 11
————————————— = ————————
2 2
5.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(12d-11) - ((4d-13)) 8d + 2
———————————————————— = ——————
2 2
6.1 Pull out like factors :
8d + 2 = 2 • (4d + 1)
4d + 1 = 0
4d + 1 = 0
7.1 Solve : 4d+1 = 0
Subtract 1 from both sides of the equation :
4d = -1
Divide both sides of the equation by 4:
d = -1/4 = -0.250
Answer:
d = -1/4 = -0.250
Step-by-step explanation:
Determine the slope of the lines parallel and perpendicular to -4x+3y=11
Answer:
parallel = 4/3
perpendicular =-3/4
Step-by-step explanation:
Solve for y
-4x+3y=11
Add 4x to each side
3y = 4x+11
Divide by 3
y = 4/3 x +11/3
This is in the form y = mx+b where m is the slope
m =4/3
The parallel line has the same slope
parallel slope is 4/3
The perpendicular line has a negative reciprocal slope
m = -(1 /4/3) = - 3/4
Answer:
[tex]\frac{4}{3}[/tex] and - [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
- 4x + 3y = 11 ( add 4x to both sides )
3y = 4x + 11 ( divide all terms by 3 )
y = [tex]\frac{4}{3}[/tex] x + [tex]\frac{11}{3}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{4}{3}[/tex]
Parallel lines have equal slopes, thus
slope of parallel line = [tex]\frac{4}{3}[/tex]
Give a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{4}{3} }[/tex] = - [tex]\frac{3}{4}[/tex]
Choose the best answer that represents the property used to rewrite the expression.
log5 6 − log5 3 = log5 2
Answer:
The Quotient Property.
Step-by-step explanation:
Since all three logarithms have the same base (base-5), and you are subtracting 6 and 3, to solve this all you need to do is 6 / 3 because of the Quotient Property.
You aren't multiplying anything, so you wouldn't use the Product Property.
You are not messing around with powers, so you wouldn't use the Power Property.
And you aren't using addition or multiplication, so you wouldn't use the Commutative Property.
Hope this helps!
A lake near the Arctic Circle is covered by a 222-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 333 weeks, the sheet is only 1.251.251, point, 25 meters thick. A Slope and xxx-intercept (Choice B) B Slope and yyy-intercept (Choice C) C Slope and a point that is not an intercept (Choice D, Checked) D xxx-intercept and yyy-intercept (Choice E) E y-intercept and a point that is not an intercept (Choice F) F Two points that are not intercepts
Answer:
S(t) = 2 - 0.25 t
Step-by-step explanation:
i am not explaining :> (me being lazy)
A motor is 85.4 % efficient: that is, the output is 85.4 % of the input.
What is the input if the motor delivers 10.75 hp. ( Round your answer to 1
decimal place.)
Answer:
12.6 hp
Step-by-step explanation:
output of motor = 85.4% of input of motor.
Given that motor delivers 10.75 hp, it means output of motor is 10.75hp
Using both the given conditions
10.75 = 85.4% of input of motor
=> 10.75 = 85.4/100 * input of motor
=> input of motor = 10.75*100/85.4 = 1075/85.5 hp = 12.57 hp.
Input of motor rounded to 1 decimal place = 12.6 hp