Answer:
0.4
Step-by-step explanation:
so, Katherine can do 0.1 of the job per hour. (if she needs 10 hours for the job, each hour she can do the whole divided by the time, so 1/10, which is 0.1)
if in two hours she and Marina can be done, then Marina will do 1(the whole job)-2/10 (twice as much as she can do in an hour)=0.8 of the job. So if Marina does 0.8 of the job in two hours, each hour she will do half of it: 0.4 - and this is the correct answer
the train traveled at an average speed of 48 miles per hour for the first 2 hours and at 60 miles an hour for the next hours. What was the train's average speed for the 6-hour trip? ( Average speed equals total miles divided by total time.)
Answer: 56 mph
Step-by-step explanation:
48 miles x 2 hours = 96 miles
60 miles x 4 hours = 240 miles
240 + 96 = 360 total miles
360 / 6 (hours) = 56 mph
Which fraction goes in the blank to make the comparison true?
Circle the letter of the correct answer
5/8<_________. A:5/8 B:4/8 C:6/8 or D:1/8
Blake chose A as the correct answer. How did he get that answer?
C is the correct answer. Good luck!
Can please help me with this
^^^^^^^^^^^^^^^^^^^^
The answer is:
The correct option is:
A) $74.55
Why?To calculate how much does Sonya pay for the four pairs altogether, we need to calculate the original price after the 50% discount and the taxes.
Calculating we have:
[tex]PriceAfterDiscount=35*50(percent)=35*\frac{50}{100}\\\\35*\frac{50}{100}=35*0.5=17.5[/tex]
We have that before the tax, the price of the shoes was $17.5, then, calculating the price after the taxes, we have:
[tex]AfterTaxes=17.5(1+6.5(percent))=17.5(1+\frac{6.5(percent)}{100})\\\\AfterTaxes=17.5(1+\frac{6.5(percent)}{100})=17.5*(1+0.065)\\\\AfterTaxes=17.5*(1+0.065)=17.5*1.065=18.637[/tex]
So, we have that the price after discount and the taxes is $18.637 per each pair of shoes.
Hence, the price for the four pairs of shoes will be:
[tex]TotalPrice=4*18.637=74.548=74.55[/tex]
Have a nice day!
a symmetrical distribution can help one calculate:
A. different probabilities
B. right angles
C. surface area
D. polynomials
Answer:
A. different probabilities
Allison pays all her bills using her bank's online bill pay. This is considered to be what type of electronic banking service?
Answer:
Transactional service
Step-by-step explanation:
If Allison pays all her bills using her bank's online bill pay, it will be considered as transactional service which is a type of electronic banking service.
A transaction involves paying a supplier for its services provided or any goods delivered.
Here the services used will include electricity, water, internet, gas, etc for which the bills are paid. Therefore, the correct answer is transactional service.
Answer:
Transaction service
Step-by-step explanation:
If alpha and beta are the zeroes of the polynomial f(x)=x2- p(x+1) - c show that (alpha+1) (Beta +1) = 1-c
Answer:
see explanation
Step-by-step explanation:
Given
f(x) = x² - p(x + 1) - c
= x² - px - p - c ← in standard form
with a = 1, b = - p and c = - p - c
Given that α and β are the zeros of f(x), then
α + β = - [tex]\frac{b}{a}[/tex] and αβ = [tex]\frac{c}{a}[/tex], thus
α + β = - [tex]\frac{-p}{1}[/tex] = p , and
αβ = [tex]\frac{-p-c}1}[/tex] = - p - c
-----------------------------------------------------------
(α + 1)(β + 1) ← expand factors
= αβ +α + β + 1 ← substitute values from above
= - p - c + p + 1
= - c + 1 = 1 - c ← as required
Final answer:
By applying Vieta's formulas to the given polynomial, we can determine that the product (α + 1)(β + 1) equals 1 - c.
Explanation:
Given the polynomial f(x) = x2 - p(x + 1) - c, whose zeroes are alpha (α) and beta (β), we can use the relationship between the coefficients of a polynomial and its zeroes to find the value of (α + 1)(β + 1). According to Vieta's formulas for a second-degree polynomial ax2 + bx + c = 0, the sum of its roots (-b/a) is equal to α + β, and the product of its roots (c/a) equals αβ.
For this specific polynomial, a = 1, b = -p, and c = -c. Thus, we have:
α + β = p
αβ = -c
Now, let's calculate (α + 1)(β + 1):
(α + 1)(β + 1) = αβ + α + β + 1 = (-c) + (p - 1) + 1 = 1 - c
Mario transferred a balance of $6050 to a new credit card at the beginning of
the year. The card offered an introductory APR of 3.1% for the first 3 months
and a standard APR of 20.6% thereafter. If the card compounds interest
monthly, which of these expressions represents Mario's balance at the end of
the year? (Assume that Mario will make no payments or new purchases
during the year, and ignore any possible late payment fees.)
Answer:
[tex]6050(1+\frac{0.031}{12})^{3}(1+\frac{0.206}{12})^{9}[/tex]
Step-by-step explanation:
p = $6050
The card offered an introductory APR of 3.1% for the first 3 months
r = 3.1% or 0.031
t = 3
n = 12
So, compound interest formula for this period is :
[tex]6050(1+\frac{0.031}{12})^{3}[/tex]
And a standard APR of 20.6% thereafter,
r = 20.6% or 0.206
t = 9
n = 12
So, compound interest formula for this period is :
[tex]6050(1+\frac{0.206}{12})^{9}[/tex]
Now as the p is common, we can re write the expressions as :
[tex]6050(1+\frac{0.031}{12})^{3}(1+\frac{0.206}{12})^{9}[/tex]
I don’t know how to do this
first off, let's recall that supplementary angles are just two sibling angles that add up to 180°.
so we have ∡T and ∡S, but we also know that ∡T = 3∡S, namely T = 3S.
[tex]\bf T+S=180\implies \stackrel{T}{3S}+S=180\implies 4S=180\implies S=\cfrac{180}{4}\implies S=45 \\\\\\ T=3S\implies T=3(45)\implies T=135[/tex]
I Need Help Pwease :->
******************************
Answer:
Area: 135 ft^2
Perimeter: 50 ft
Step-by-step explanation:
area:
take the rectanle so length 12 x 9 = 108 so that is the length of the rectangle and now we need to find that of the triangle left over
subract 18 - 12 = 6 so that is the base of the trianle and we know the side length is 9 so plus it in A = (9)(6)/2
A = 54/2
A = 27
add 27 + 108 to get the total area
135
perimeter:
18 + 9 + 11 + 12 = 50
For this case we have that by definition, the perimeter of the trapezoid is given by the sum of its sides:
[tex]p = 9 + 18 + 11 + 12\\p = 50[/tex]
So, the perimeter is 50ft
On the other hand, the area is given by:
[tex]A = \frac {1} {2} (b_ {1} + b_ {2}) * h[/tex]
Where:
[tex]b_ {1}:[/tex] It is the largest base
[tex]b_ {2}:[/tex] It is the minor base
h: It's the height
Substituting the values:
[tex]A = \frac {1} {2} (18 + 12) * 9\\A = \frac {1} {2} (30) * 9\\A = \frac {1} {2} (270)\\A = 135[/tex]
So, the area of the trapezoid is [tex]135 \ ft ^ 2[/tex]
Answer:
the perimeter is 50ft
the area of the trapezoid is [tex]135 \ ft ^ 2[/tex]
How many 4-letter passords can be made using the letters A thought Z if...
a) Repetition of letters is allowed?
b) Repetition of letters is not allowed?
Answer:
a.)The total 4-letters passwords when repetition of letters is allowed are 456976
b.)The total 4-letters passwords when repetition of letters is not allowed are 358800
Step-by-step explanation:
Some situations of probability involve multiple events. When one of the events affects others, they are called dependent events. For example, when objects are chosen from a list or group and are not returned, the first choice reduces the options for future choices.
There are two ways to sort or combine results from dependent events. Permutations are groupings in which the order of objects matters. Combinations are groupings in which content matters but order does not.
How many 4-letter passwords can be made using the letters A throught Z if...
a)Repetition of letters is allowed?
There are only 26 possible values for each letter of the password (The English Alphabet consists of 26 letters). The total 4-letters passwords when repetition of letters is allowed are [tex]26^{4} =456976[/tex]
b) Repetition of letters is not allowed?
If repetition of letters is not allowed, we can only choose 4 letters out of 26. Using the permutation equation [tex]nP_{k} =\frac{n!}{(n-k)!}[/tex]
The total 4-letters passwords when repetition of letters is not allowed are [tex]26P_{4} =\frac{26!}{(26-4)!}=26.25.24.23=358800[/tex]
.
When repetition of letters is allowed, there are 456,976 possible 4-letter passwords that can be made using the letters A through Z. When repetition of letters is not allowed, there are 358,800 possible passwords that can be made.
Explanation:a) When repetition of letters is allowed, we have 26 choices for each of the 4 positions in the password. Therefore, the number of 4-letter passwords that can be made is 26 * 26 * 26 * 26 = 456,976.
b) When repetition of letters is not allowed, the number of choices for the first position is 26. For the second position, there are 25 choices left, since we can't repeat the letter used in the first position. Similarly, for the third position, there are 24 choices, and for the fourth position, there are 23 choices. Therefore, the number of 4-letter passwords that can be made without repetition is 26 * 25 * 24 * 23 = 358,800.
Learn more about 4-letter passwords here:https://brainly.com/question/19866551
#SPJ3
Yumi is determining the seating arrangement for a big dinner party.circular tables will seat 8 guests and rectangular tables can seat 10 guests write and inequality that describes the situation let X=# of a circular tables let y =# of rectangular tables
The volumes of two similar figures are 27 mm3 and 1331 mm3. If the surface area of the smaller figure is 18 mm2, what is the surface area of the larger figure?
Answer:
242 mm²
Step-by-step explanation:
Given 2 similar figures with
ratio of sides = a : b, then
ratio of areas = a² : b² and
ratio of volumes = a³ : b³
Here the ratio of volumes = 27 : 1331, hence
ratio of sides = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{1331}[/tex] = 3 : 11, thus
ratio of areas = 3² : 11² = 9 : 121
let x be the surface area of the larger figure then by proportion
[tex]\frac{18}{9}[/tex] = [tex]\frac{x}{121}[/tex] ( cross- multiply )
9x = 18 × 121 ( divide both sides by 9 )
x = [tex]\frac{18(121)}{9}[/tex] = 2 × 121 = 242
The surface area of the larger figure is 242 mm²
Find the exact values of the six trigonometric functions for angle e in standard position if a point with the coordinates (-6, 6) lies
on its terminal side.
13
Note: A value such as = can be entered as sr3/2.
Answer:
tan e = -1
cot e = -1
sin e = √2/2
cosec e = √2
cos e = -√2/2
sec e = -√2.
Step-by-step explanation:
6/6- is the tangent of e so tan e = -1.
cot e = 1/tan e = -1.
The hypotenuse of the triangle containing angle e = √(-6)^2 + (6)^2 ( By the pythagoras theorem) and = √72 = 6√2.
Therefore sin e = 6/6√2
= 1/√2
= √2/2
cosec e = 1 ./ sin e = √2.
cos e = -6 / 6√2
= -√2/2.
sec e = 1/cos e = -√2.
I NEED THE ANSWER FAST!!!!
Answer:
I think it’s 28 but I’m not sure
(sorry if it’s wrong)
Step-by-step explanation:
Which graph shows the quadratic function y = 3x2 − 12x + 10? (5 points)
ANSWER
The graph in option D.
EXPLANATION
The given function is:
[tex]y = 3 {x}^{2} - 12x + 10[/tex]
We complete the square to obtain:
[tex]y = 3( {x}^{2} - 4x) + 10[/tex]
[tex]y = 3( {x}^{2} - 4x + {( - 2)}^{2} ) + 10 - 3 {( - 2)}^{2}[/tex]
[tex]y = 3{( x- 2)}^{2}+ 10 - 12[/tex]
[tex]y = 3{( x- 2)}^{2} - 2[/tex]
The graph of this function opens upwards and has its vertex at (2,-2).
The y-intercept is 10.
From the options the graph that satisfies all these properties is D.
F(x)=(1/4)^x+1 graph
Answer:
Step-by-step explanation:
g(x) to g(x)=-[x]+3 what is the domain of g(x)?
Final answer:
The domain of the function g(x) = -[x] + 3 is all real numbers because the floor function is defined for all real numbers.
Explanation:
The given function is g(x) = -[x] + 3. To determine the domain of g(x), we look for the set of all input values (x) that the function can accept.
The square brackets around x indicate that we are dealing with the floor function, which takes a real number and rounds it down to the nearest integer.
Since the greatest integer function is defined for all real numbers, the only restriction we have is when the function involves division by zero.
Since the process of rounding down to the nearest integer is defined for all real numbers, the domain of g(x) is all real numbers, which is expressed as ∞ < x < ∞ or –∞ < x < ∞.
is it possible for a trapezoid to have only 3 right angles
No, if you were to have three right angles, the fourth angle would also have to be a right angle. As a result, it would make the shape either a square or a rectangle.
A news station in Oregon recorded that the low temperatures for 5 days were –3, –2, 2, 2, and 6. What was the average temperature for those days?
Answer:
Average = 1
Step-by-step explanation:
Let us define the average first:
Average is calculated by adding up all the values and then dividing the sum by total number of values.
The formula for average may be written as:
[tex]Average = \frac{Sum}{count}[/tex]
In the following case,
Sum of numbers = -3-2+2+2+6 = 5
Count = 5
So,
Average = 5/5
=> Average = 1
Answer:
the answer is 1
Step-by-step explanation:
Sum of numbers = -3-2+2+2+6 = 5
Count = 5
So,
Average = 5/5
=> Average = 1
If y is 5 when x is 2.5 and y varies directly with x, find y when x is 10.
Answer:
Step-by-step explanation:
Y=20. X=10. Y=5. X=2.5
X is half of Y so 20 is y
Answer:
20
Step-by-step explanation:
Find the value of y.
Answer: Second option.
Step-by-step explanation:
By the Right Triangle Altitude Theorem, we know that the altitude "h" (Observe the figure attached) is:
[tex]h=\sqrt{9*3}\\h=3\sqrt{3}[/tex]
Then, since we know the value of the altitude, we can calculate the value of "y" with the Pythagorean Theorem:
[tex]a=\sqrt{b^2+c^2}[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.
We can identify that:
[tex]a=y\\b=9\\c=h=3\sqrt{3}[/tex]
Then, substituting values, you get that "y" is:
[tex]y=\sqrt{9^2+(3\sqrt{3})^2}=6\sqrt{3}[/tex]
Solve
-2x+8=14
3
-11
-3
11
Answer:
-3
Step-by-step explanation:
-2x+8=14
Subtract 8 from each side
-2x+8-8=14-8
-2x = 6
Divide by -2
-2x/-2 = 6/-2
x = -3
-2x + 8 = 14
Step 1: Bring 8 to the right side of the equation. To do this subtract 8 to both sides (this is the opposite of addition and will cancel 8 from the left side)
-2x + (8 - 8) = 14 - 8
-2x + 0 = 6
-2x = 6
Step 2: Isolate x by dividing -2 to both sides (division is the opposite of multiplication and will cancel -2 from the left side)
-2x/-2 = 6/-2
x = -3
Check:
Plug -3 where you see x and solve
-2(-3) + 8 = 14
6 + 8 = 14
14 = 14...............................Correct!
Hope this helped!
given the parent function f(x)=x^2 describe the graph of y=(x-5)^2-2
Step-by-step explanation:
Shift to the right 5 units and down 2 units.
What is the relationship between 1 meter and 1 centimeter?
Answer: 100 cm = 1 m
Step-by-step explanation:
Like most metric measurements, 100 centimeters are equal to 1 meter.
Question 3 of 10
1 Point
Which of the following are equations for the line shown below? Check all that
apply.
(2, 2)
DA y- 5 = 1.5(x-4)
O B. y=1.5x-1
C. y-4 = 1.5(x-5)
D. y-2 = 1.5(x-2)
Answer:
A. [tex]y-5=1.5(x-4)[/tex].
B. [tex]y=1.5x-1[/tex].
Step-by-step explanation:
The given line passes through (2,2) and (4,5).
The slope the given line can be found using the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{5-2}{4-2}[/tex]
This gives [tex]m=\frac{3}{2}=1.5[/tex].
The slope-intercept form is [tex]y-y_1=m(x-x_1)[/tex].
We substitute the second point to get:
[tex]y-5=1.5(x-4)[/tex].
We expand to get:
[tex]y-5=1.5x-6[/tex].
[tex]y=1.5x-6+5[/tex].
[tex]y=1.5x-1[/tex].
What is the area of the rectangle?
Answer:
60cm^2
Step-by-step explanation:
5 * 12 = 60cm^2
Plz help in solving these 2 questions with steps and explanation!!
Answer:
[tex]\large\boxed{Q1:\ x=2\ or\ x=5}\\\boxed{Q2:\ x=1-\sqrt{21}\ or\ x=1+\sqrt{21}}[/tex]
Step-by-step explanation:
[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=0\\\\\text{If}\ b^2-4ac<0,\ \text{then the equation has}\ \bold{no\ solution}\\\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\==========================================[/tex]
[tex]\bold{Q1}\\\\x^2-7x+10=0\\\\a=1,\ b=-7,\ c=10\\\\b^2-4ac=(-7)^2-4(1)(10)=49-40=9>0\\\\\sqrt{b^2-4ac}=\sqrt9=3\\\\x_1=\dfrac{-(-7)-3}{2(1)}=\dfrac{7-3}{2}=\dfrac{4}{2}=2\\\\x_2=\dfrac{-(-7)+3}{2(1)}=\dfrac{7+3}{2}=\dfrac{10}{2}=5\\\\========================================[/tex]
[tex]\bold{Q2}\\x^2-2x=20\qquad\text{subtract 20 from both sides}\\\\x^2-2x-20=0\\\\a=1,\ b=-2,\ c=-20\\\\b^2-4ac=(-2)^2-4(1)(-20)=4+80=84>0\\\\\sqrt{b^2-4ac}=\sqrt{84}=\sqrt{4\cdot21}=\sqrt4\cdot\sqrt{21}=2\sqrt{21}\\\\x_1=\dfrac{-(-2)-2\sqrt{21}}{2(1)}=\dfrac{2-2\sqrt{21}}{2}=1-\sqrt{21}\\\\x_2=\dfrac{-(-2)+2\sqrt{21}}{2(1)}=\dfrac{2+2\sqrt{21}}{2}=1+\sqrt{21}[/tex]
Answer:
Step-by-step explanation:
x^2 - 7x + 10 = 0 can be factored as follows: (x - 5)(x - 2). Note that -5x -2x combine to -7x, the middle term of this quadratic, and that (-5)(-2) = +10, the constant term. Setting each of these factors = to 0 separately, we get:
x = 5 and x = 2.
x^2 - 2x = 20 should be rewritten in standard form for a quadratic equation before you attempt to solve it: x^2 - 2x - 20 = 0. This quadratic is not so easily factored as was the previous one. Let's use the quadratic formula:
-b ± √(b²-4ac)
x = --------------------
2a
Here, a = 1, b = -2 and c = -20, so the discriminant b²-4ac = (-2)^2 - 4(1)(-20), or 4 + 80, or 84. 84 has only one perfect square factor: 4·21. Because the discriminant is +, we know that this equation has two real, unequal roots.
They are:
-(-2) ± √(4·21) 2 ± 2√21
x = ---------------------- = ----------------- = 1 ± √21
2(1) 2
What is the multiple zero and multiplicity of f(x)=x^3+2x^2+x? Help needed !!
A. Multiple zero =-1; multiplicity = 2
B. Multiple zero =1;multiplicity =2
C. Multiple zero = 2; multiplicity =-1
D. Multiple zero =2; multiplicity =1
f(x) = x³ + 2x² + x
f(x) = x.(x² + 2x + 1)
f(x) = x.(x + 1)²
So, f(x) = 0 when x = 0 or when x = -1
But
f(x) = x.(x + 1)² = x.(x + 1).(x + 1)
So we have three roots, x = 0, x = -1 and x = -1, although two of them are equal.
So we have a multiple zero x = -1 with a multiplicity 2.
Alterativa A.
Answer:
A
Step-by-step explanation:
The length of a rectangle is 5 units and its width is 4 units. What is the approximate length of the diagonal of the rectangle?
A) 5 units
B) 6.4 units
C) 8.5 units
D) 9 units
Answer:
b
Step-by-step explanation:
using pythagoras theorem:
d=(5^2+4^2)^1/2
=6.4 units
Answer:
The approximate length of the diagonal of the rectangle = 6.4 units ⇒ B
Step-by-step explanation:
* Lets revise the properties of the rectangle
- The rectangle has 4 sides
- Each two opposite sides are parallel and equal in length
- It has for right angles
- Its two diagonals are equal in length
- The diagonal divide the rectangle into two congruent right triangles
* Now lets solve the problem
∵ The length of the rectangle = 5 units
∵ The width of the rectangle = 4 units
∵ The diagonal of the rectangle with the length and the width formed
right triangle, the length and the width are its two legs and the
diagonal is its hypotenuse
- To find the length of the hypotenuse use Pythagoras theorem
∵ Hypotenuse = √[(leg1)² + (leg2)²]
∴ The length of the diagonal = √[5² + 4²] = √[25 + 16] = √41
∴ The approximate length of the diagonal of the rectangle = 6.4 units