Answer:
Solve for x: 3[2^(x-3) ]=384:solution:
Here,3[ 2^(x-3) ] = 384
or, 2^(x-3) = ( 384 /3 )
or, 2^(x-3) = 128
or, 2^(x-3) = 2^(7)
or, x-3 = 7 [ ∵ laws of indices ]or, x = 7+3
∴ x = 10 ans
Find the difference of 7,419 and 5,267
Answer:
2,152
Step-by-step explanation:
So to find this all you have to do is subract 7,419 and 5,267 to get the answer of 2,152
Hope This Helps <3 <3
A Native American tepee is a conical tent. Find the number of skins needed to cover a teepee 10 ft. in diameter and 12 ft. high. Each skin covers 15 sq. ft. (use = 3.14)
Since it is conical, we need to find the surface area of the top of the conical shape.
If we unfold the top part of the cone, we will have a section of a circle:
The circunference of this section is the same as the total circunference of the base of the cone, which we can get from its radius (half its diamtere):
[tex]C=2\pi r=2\pi\cdot\frac{D}{2}=2\pi\cdot\frac{10}{2}=10\pi[/tex]If we visualize the cone by the side, we see that it forms a isosceles triangle which the same height and the base euqal to the diameter:
So, we can calculate "R", the radius of the unfolded cone, using the Pythagora's Theorem:
[tex]\begin{gathered} R^2=h^2+(\frac{D}{2})^2 \\ R^2=12^2+5^2 \\ R^2=144+25 \\ R^2=169 \\ R=\sqrt[]{169} \\ R=13 \end{gathered}[/tex]The circunference of a section of a circle is the circunferece of the total circle times the fraction of the section represents of the total circle. Let's call ths fraction "f", this means that:
[tex]\begin{gathered} C_{total}=f\cdot C \\ C_{total}=2\pi R=2\pi\cdot13=26\pi \\ C=10\pi \\ f\cdot26\pi=10\pi \\ f=\frac{10\pi}{26\pi}=\frac{5}{13} \end{gathered}[/tex]The area will follow the same, the area of the section is the fraction "f" times the total area of the circle, so:
[tex]\begin{gathered} A_{total}=\pi R^2=\pi13^2=169\pi \\ A=f\cdot A_{total}=\frac{5}{13}\cdot169\pi=65\pi\approx65\cdot3.14=204.1 \end{gathered}[/tex]So, the surface area of the top of the cone is 204.1 ft². Since each skin covers 15 ft², we can calculate how many skins we need by dividing the total by the area of each skin:
[tex]\frac{204.1}{15}=13.60666\ldots[/tex]This means that we need 13.60666... skins, that is, 13 is not enough, we need one more, so we need a total of 14 skins.
use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. If two orders are selected, find the probability that they are both accurate. Complete parts (a) and (b) below.
a. Assume that the selections are made with replacement. Are the events independent?
The probability is __. The events __ (are, are not) independent.
(Do not round until the final answer. Round to four decimal places as needed.)
Answer:
a. If the selection is made with replacement, they are NOT independent because they affect each other.
b. The probability of selecting TWO accurate orders is .7157 and the events ARE independent.
Step-by-step explanation:
Add the accurate orders:
315+273+248+125=961
Add the inaccurate orders:
38+56+37+17=148
148/961=0.1540 probability of getting ONE inaccurate order
1.0-0.1540=0.846 probability of selecting ONE accurate order
0.846 * 0.846 = 0.7157 the probability of selecting TWO accurate orders
Therefore, the probability is .7157 and the events ARE independent.
can you help me answer this please?This is condense each expression to a sinhle logarithm
ANSWER
[tex]\log_3x^{\frac{1}{3}}[/tex]EXPLANATION
Given;
[tex]\frac{\log _3x}{3}[/tex]Rewrite as;
[tex]\frac{1}{3}\log_3x[/tex]Simplify by moving 1/3 inside the logarithm;
[tex]\begin{gathered} \log_3x^{\frac{1}{3}} \\ \end{gathered}[/tex]i need help with a test prep problem
The diameter = 2 times the radius
radius = diameter / 2
radius = 25.3/2
radius = 12.65 cm
Result radius = 12.65 cm
simplified 4/16 (all fractions)
Answer:
The greatest common factor (GCF) of the numerator (4) and the denominator (16) is 4
GCF(4,16) = 4
4/16 = 4 ÷ 4/16 ÷ 4
= 1/4
hope it helps you
he graphs of the functions and are shown below. For each graph, find the absolute maximum and absolute minimum.
From the given graph
The graph of g has an arrow with the left end it goes up, then
The absolute maximum of g is NONE
The graph of g has a minimum point (4, -4), then
The absolute minimum is -4
The graph of h has a maximum point (-4, 4), then
The absolute maximum is 4
The graph of h has a minimum point (-1, -4), then
The absolute minimum is -4
THIS IS URGENT!!!! PLEASE HELP!!!
The amount of flour needed for 72 cookies is 4.5 cups.
46 / 69 and 48/84 are not proportional because the fractions in their simplest forms are 3/4 and 4/7.
The value of x in 2/3 = 1.2 / x is 1.8.
The value of x in 8 / 15 = 24 / x is 45.
7 / 5 ≠ 15 / 10.
6 / 8 = 15/20
What are the solutions?In order to determine how many cups of flour is needed for 72 cookies, determine how many cups is needed for one cookies.
Amount of flour needed for one cookie = 3/48
Now, multiply this fraction by 72: 3/48 x 72 = 4.5 cups
If two fractions are proportional, when they are expressed in their simplest form, both fractions would have equal values.
46 / 69 = 2 / 3
48 / 84 = 4/7
Given this equation : 2/3 = 1.2 / x
In order to determine the value of x, cross multiply:
2x = 3 x 1.2
2x = 3.6
x = 3.6 / 2
x = 1.8
Given this equation : 8 / 15 = 24 / x
In order to determine the value of x, cross multiply:
8x = 24 x 15
8x = 360
x = 360 / 8
x = 45
7/5 and 15 / 10
7/5 = 15 /10
The cross product:
(7 x 10) = (5 x 15)
70 ≠ 75
6 / 8 = 15/20
The cross product : (6 x 20) = (8 x 15)
120 = 120
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2.8-4.4n-2n+7QUICKLY BRAINLY IF CORRECT
Answer
2.8 - 4.4n - 2n + 7 = 9.8 - 6.4n
Explanation
To answer this, we just bring the terms with n together and the terms without together too.
2.8 - 4.4n - 2n + 7
= 2.8 + 7 - 4.4n - 2n
= 9.8 - 6.4n
Hope this Helps!!!
Find the quotient of 24 and 3.
Please help
Answer
8
Step-by-step explanation
we know that the term quotient means that we divided so we think backward if 24 is being divided by 3 what times 3 equals 24 the answer would be 8 because 3x8=24.
i can provide a better picture if needed but i only need help with b
Taking a look at the graph, we can notice that point (7000,2875.99) is highlighted.
Using this point, we can conclude that the cost of talking 7000 minutes is $2875.99
It takes Anastasia 45 minutes to walk 2.5 miles to the park. At this rate, how
many minutes should it take her to walk 3 miles?
please help with this practice question
Would the answer be 2? I multiplied the coordinate (3, 6) by two and got ( 6, 12), I don't know if I'm right
Since we would need to multiply each coordinate by 1/2 to perform the transformation, then the scale factor would be 1/2. The answer is the first option.
I have a practice problem that I need answered, can someone help and explain?
Given:-
[tex]\begin{gathered} A=\begin{bmatrix}{-3} & {5} & {2} \\ {8} & {-1} & {3} \\ {} & {} & \end{bmatrix} \\ \end{gathered}[/tex]Now to find the value of,
[tex]-2R_2+3R_1[/tex]So by simplyfying according to the given elementary row operation,
The Smith’s and the Jones are neighbors. They both have a tax rate of 28.5 mills. The Smith’s house is assessed at $80,000. The Jones’ house is assessed at $67,000. How much more do the Smith’s pay in property tax?
Given
Tax rate = 28.5 mills
Smith's house is accessed at $80,000
Jones's house is accessed at $67,000
Property taxes are calculated by multiplying the assessed, taxable property value by the mill rate and then dividing that sum by 1,000.
The formula is given by:
[tex]Property\text{ tax levied on property = }\frac{mill\text{ rate }\times taxable\text{ property value}}{1000}[/tex]Property tax for the Smith's:
[tex]\begin{gathered} =\text{ }\frac{28.5\text{ }\times\text{ 80000}}{1000} \\ =\text{ 2280} \end{gathered}[/tex]Property tax for the Jones':
[tex]\begin{gathered} =\frac{28.5\text{ }\times\text{ 67000}}{1000} \\ =\text{ 1909.5} \end{gathered}[/tex]The extra amount the Smith's pay is the difference in the tax levied on Smith and Jones:
[tex]\begin{gathered} =\text{ 2280 - 1909.5} \\ =\text{ 370.5} \end{gathered}[/tex]Hence, the Smith's pay $370.5 more than the Jones'
The formula A = P +Prt represents the relationshipbetween the principal, P, interest rate, r, and amount ofmoney, A, in an account over a period of time, t.Solve the equation for P.
Problem
The formula A = P +Prt
Solution
We can take common factor and we got:
A= P(1+rt)
And we can divide both sides by 1+rt and we got:
P = A /(1+rt)
The projected profit (in thousands of dollars) of a new technology company in year t can be modeled by the polynomial 2t2 - 9t - 18
When the company will break even (have zero profit)? Show all work necessary to justify your answer.
The projected profit (in thousands of dollars) in year t of a newly developed line of business can be modeled by the monomial t3 . Write a polynomial that models the company’s total profit including this new line of business.
How many years sooner will the company break even with the new line of business? Show all work necessary to justify your answer.
a. The company will break even in 6 years
b. The total profit with the newly developed line of business is:
[tex]t^3+2t^2-9t-18[/tex]c. The company will break even 3 years sooner
Explanation:The projected profit is given as:
[tex]2t^2-9t-18[/tex]a. The company will break even when the profit is zero. That is;
[tex]\begin{gathered} 2t^2-9t-18=0 \\ \\ (2t+3)(t-6)=0 \\ 2t+3=0 \\ \Rightarrow t=-\frac{3}{2} \\ \\ t-6=0 \\ t=6 \end{gathered}[/tex]6 is the realistic number of years (As we cannot have -3/2 years).
We conclude that they will break even in 6 years
b. The projected profit of a newly developed line of business is:
[tex]t^3[/tex]The total profit is now;
[tex]t^3+2t^2-9t-18[/tex]The company will break even with this new line of business as follows:
[tex]\begin{gathered} t^3+2t^2-9t-18=0 \\ (t+2)(t+3)(t-3) \\ t+2=0 \\ \Rightarrow t=-2 \\ t+3=0 \\ \Rightarrow t=-3 \\ t-3=0 \\ \Rightarrow t=3 \end{gathered}[/tex]We choose t = 3 (because we cannot have -2 years or -3 years)
The difference between this and the previous time is 6 - 3 = 3 years
The company will break even 3 years sooner
Pt 2. ROOTS OF QUADRATICS 50 PT!!!
Using the discriminant of a quadratic function, it is found that:
6. The range of values is of c ≤ 1/16.
8. The range of values of k is: -9 < k < -1.
10. The discriminant is never negative, hence the function has real roots for all values of k.
Discriminant of a quadratic functionA quadratic function is modeled as follows:
y = ax² + bx + c.
The discriminant of the function is given as follows:
Δ = b² - 4ac
For item 6, the function is given as follows:
y = 2x² - 3x + (2c + 1).
The coefficients are given as follows:
a = 2, b = -3, c = 2c + 1.
The function is positive for all values of x if it has at most one real root, hence:
Δ ≥ 0
(-3)² - 4(2)(2c + 1) ≥ 0
9 - 16c - 8 ≥ 0
1 - 16c ≥ 0
16c ≤ 1
c ≤ 1/16
For item 8, the function is given as follows:
y = kx² - (k - 3)x - 1 = 0.
The coefficients are given as follows:
a = k, b = -k - 3, c = -1.
It has no real roots if:
Δ < 0
b² - 4ac < 0
(-k - 3)² - 4(k)(-1) < 0
k² + 6x + 9 + 4k < 0
k² + 10k + 9 < 0
Hence the range is:
-9 < k < -1.
For item 10, the function is given as follows:
y = kx² + (k - 2)x - 2 = 0.
The coefficients are given as follows:
a = k, b = k - 2, c = -2.
It has no real roots if:
Δ < 0
b² - 4ac < 0
(k - 2)² - 4(k)(-2) < 0
k² - 4k + 4 + 8k < 0
k² + 4k + 4 < 0
(k + 2)² < 0.
(k + 2)² is always positive, hence the function will always have real roots.
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Answer
Discriminant of a quadratic functio
A quadratic function is modeled as follows:
y = ax² + bx + c.
The discriminant of the function is given as follows:
Δ = b² - 4ac
For item 6, the function is given as follows:
y = 2x² - 3x + (2c + 1).
The coefficients are given as follows:
a = 2, b = -3, c = 2c + 1.
The fnction is positive for all values of x if it has at most one real root, hence:Δ ≥ 0
(-3)² - 4(2)(2c + 1) ≥ 0
9 - 16c - 8 ≥ 0
1 - 16c ≥ 0
16c ≤ 1
c ≤ 1/16
For item 8, the function is given as follows:
y = kx² - (k - 3)x - 1 = 0.
The coefficients are given as follows:
a = k, b = -k - 3, c = -1.
It has no real roots if:
Δ < 0
b² - 4ac < 0
(-k - 3)² - 4(k)(-1) < 0
k² + 6x + 9 + 4k < 0
k² + 10k + 9 < 0
Hence the range is:
-9 < k < -1.
For item 10, the function is given as follows:
y = kx² + (k - 2)x - 2 = 0.
The coefficients are given as follows:
a = k, b = k - 2, c = -2.
It has no real roots if:
Δ < 0
b² - 4ac < 0
(k - 2)² - 4(k)(-2) < 0
k² - 4k + 4 + 8k < 0
k² + 4k + 4 < 0
(k + 2)² < 0.
(k + 2)² is always positive, hence the function will always have real roots.
Step-by-step explanation:
Which is a perfect square?A:72B:81C:90D:99
Solution:
A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer.
Hence, the number that can be expressed as a product of an integer by itself is;
[tex]81=9^2=9\times9[/tex]Therefore, the perfect square is 81.
OPTION B is correct.
3 people share one sandwich equally. what fraction of the sandwich will each person get? show work and write and equation. & solution
Let each person get portion "x".
So, 3 person would get "3x" and that would be equal to "1" sandwich.
Thus, we can write the equation:
[tex]3x=1[/tex]Let's solve for "x",
[tex]\begin{gathered} 3x=1 \\ x=\frac{1}{3} \end{gathered}[/tex]Each person will get one-third of a sandwich.
g(x)=-3x-1 What is g(10
A function is a relation that gives one input for every one output thus the value of g(10) is -31.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given function,
g(x) = -3x - 1
The value of the function at x = 10
g(10) = -3(10) - 1
g(10) = -30 - 1 = -31
Hence "A function is a relation that gives one input for every one output thus the value of g(10) is -31".
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Last week, Lisa sold 20 hand-engraved watch bands, earning a total profit of $105.00.She plans to make 50 engraved watch bands to sell at the community art fair. If shesells all 50 watch bands, how much profit can Lisa expect to earn?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
hand-engraved watch bands:
total watch bands = 20
total profit = $105.00
Step 02:
ratio:
total profit (50 watch bands):
[tex]50\text{ watch bands * }\frac{\text{ \$ 105.00}}{20\text{ watch bands}}\text{ = \$ 262.50 }[/tex]The answer is:
$ 262.50
A line passes through the point (-4,-6) and has a slope of 5/4. Write an equation in slope-intercept form for this line.
Answer:
y = [tex]\frac{5}{4}[/tex] x - 1
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 )
here m = [tex]\frac{5}{4}[/tex] , then
y = [tex]\frac{5}{4}[/tex] x + c ← is the partial equation
to find c substitute (- 4, - 6 ) into the partial equation
- 6 = - 5 + c ⇒ c = - 6 + 5 = - 1
y = [tex]\frac{5}{4}[/tex] x - 1 ← equation of line
Anyone know the question ?
The total commission earned by Paun is $14,000.
What is meant by the term commission?Full-service brokerages make the majority of their money by charging commissions on customer transactions.Commission-based advisors earn money by purchasing and selling a product on their clients' behalf.Commissions and fees differ in the financial services industry, where fees are a fixed amount for managing a customer's money.For the given question.
The total sales done by Paun is $50,000.
There is commission of 25% on first $2000.
There is commission of 30% on remaining that is 48,000.
The total commission will be 25% of $2,000 and 30% of 48,000.
25% of $2,000 = 25 × 2000/100
25% of $2,000 = $500
30% of 48,000 = 30 × 48,000/100
30% of 48,000 = $14,400
Total commission = $500 + $14,400 = $14,900.
Thus, the total commission earned by Paun is $14,000.
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Businesses deposit large sums of money into bank accounts. Imagine an account with $10 million dollars in it.
a. How much would the account earn in one vear of simple interest at a rate of
2.12067 Round to the nearest cent.
The least positive number x for which cos x = 0 is "blank"
enter your response here.
(Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) TUSM!!!!!
The least positive number x for which cos x = 0 is 1.
The given trigonometric equation is cos x=0.
What is the trigonometric equation?A trigonometric equation is one that involves one or more of the six functions sine, cosine, tangent, cotangent, secant, and cosecant. Some trigonometric equations, like x = cos x, can be solved only numerically, through successive approximations.
Now, cos x = 0
So, [tex]x=cos^{-1}(0)[/tex]
⇒ x = 1
Therefore, the least positive number x for which cos x = 0 is 1.
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What’s the correct answer? I need help now
helppppppppppp meeeeeeeeeeeeeee
Answer:
A. f(-2) = 13
B. f(0) = 1
C. f(7) = -41
Step-by-step explanation:
f(x) = 1 - 6x
A.
f(-2) = 1 - 6(-2)
f(-2) = 1 + 12
f(-2) = 13
B.
f(0) = 1 - 6(0)
f(0) = 1
C.
f(7) = 1 - 6(7)
f(7) = 1 - 6(7
f(7) = -41
I hope this helps!
How do I solve this exponential function using logarithms, it says if necessary you can round to the nearest hundredth, please show work!
The given equation is
[tex](x+7)=(2x-1)[/tex]At first, we have to isolate x on one side and the numerical term on the other side, then
Add 1 to both sides
[tex]\begin{gathered} x+7+1=2x-1+1 \\ x+8=2x \end{gathered}[/tex]Subtract x from both sides
[tex]\begin{gathered} x-x+8=2x-x \\ 8=x \end{gathered}[/tex]The solution of the equation is x = 8