Final answer:
A baker would need to use 7 scoops of flour with a 1 1⁄2 cup measuring scoop to have at least 4 3⁄4 cups of flour.
Explanation:
The question at hand requires us to determine how many scoops of flour a baker would need to use to obtain at least 4 3⁄4 cups of flour with a scoop that holds 1 1⁄2 cups. To solve this, we will divide the total amount of flour needed by the capacity of the scoop:
Convert the mixed numbers to improper fractions: 4 3⁄4 cups = 19⁄4 cups and 1 1⁄2 cups = 3⁄2 cups.Now, divide 19⁄4 cups by 3⁄2 cups to find the number of scoops.19⁄4 ÷ 3⁄2 = 38⁄8 ÷ 3⁄2 = 38⁄8 x 2⁄3 = 38⁄12 x 2⁄1 = 76⁄12 = 19⁄3. This result is an improper fraction which corresponds to 6 1⁄3 scoops.Since a baker can't use a fraction of a scoop, they will need to use at least 7 full scoops to ensure they have enough flour.Therefore, the baker must use 7 scoops to have at least 4 3⁄4 cups of flour.
Find the 4th term of the expansion of (2a - b)^7.
a.
-560a^4b^3
c.
560a^4b^3
b.
-560a^3b^4
d.
560a^3b^4
Answer:
-560a^4b^3
Step-by-step explanation:
Given:
(2a - b)^7
By using Binomial theorem:
128a^7 - 448a^6b + 672a^5b^2 - 560a^4b^3 + 280a^3b^4 - 84a^2b^5 + 14ab^6-b^7
Here the fourth term is -560a^4b^3 !
Answer:
-560a^4 b^3.
Step-by-step explanation:
The (r + 1)th term of (a + x)^n = nCr a^(n-r) x^r.
So, the 4th term of (2a - b)^7 = 7C3 (2a)(7-3)x^3
= 35*16a^4(-b)^3
= -560a^4 b^3.
At a game show, there are 8 people (including you and your friend) in the front row. The host randomly chooses 3 people from the front row to be contestants. The order in which they are chosen does not matter. How many ways can you and your friend both be chosen?
There are 2 ways that you and your friend can both be chosen as contestants.
Explanation:The question is on the concept of probability. There are 8 people in the front row, including you and your friend.
The host randomly chooses 3 people to be contestants.
The order in which they are chosen does not matter.
Since you and your friend are both in the front row, there are 2 cases where you both can be chosen: either you are chosen and your friend is chosen, or your friend is chosen and you are chosen.
So the total number of ways you and your friend can both be chosen is 2.
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Aaron is in his math class. His teacher says that class will be dismissed when the minute hand makes a 90° clockwise rotation. What time will it be when the teacher dismisses the class?
4:05
3:35
3:25
3:20
3:55
Answer:
3:20
Step-by-step explanation:
The 360 degrees clockwise rotation of the minute hand corresponds to 60 minutes.
The 90 degrees clockwise rotation is one-fourth of the 360 degrees, and hence will corresponds to 15 minutes.
The time is now 3:05.
After 15 minutes the time will be 3:20
Therefore the teacher dismisses the class at 3:20
Sunny earns \$12$12dollar sign, 12 per hour delivering cakes. She worked for xxx hours this week. Unfortunately, she was charged \$15$15dollar sign, 15 for a late delivery on Tuesday. How much money did Sunny earn this week?
Answer:
12x - 15 dollars
Step-by-step explanation:
Sunny earns $12 per hour for delivering cakes.
She worked for x hours this week.
Unfortunately, she was charged $15 for a late delivery on Tuesday
She was supposed to earn $12 × x = $12x this week
But she was charged $15 for late delivery on Tuesday
So her net earning this week is; $12x - $15
Answer:
12x-15
Step-by-step explanation:
Please help me out please
Answer:
[tex]\frac{8}{81}[/tex]
Step-by-step explanation:
Since the sequence is geometric there is a common ratio r between consecutive terms.
r = [tex]\frac{1}{3}[/tex] ÷ [tex]\frac{1}{2}[/tex]
= [tex]\frac{1}{3}[/tex] × [tex]\frac{2}{1}[/tex] = [tex]\frac{2}{3}[/tex]
Multiplying [tex]\frac{4}{27}[/tex] by r gives the next term in the sequence
[tex]\frac{4}{27}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{8}{81}[/tex]
You purchase 4 large pizzas for lunch on the beach.Each one cost 9.50$. How much do u spend on pizza
Answer:
$38.00
Step-by-step explanation:
You purchase 4 large pizzas.
Each one costs $9.50
Total expenditure on pizza = $9.50 × 4 = $38.00
4 times 9.50 would be 38. So you will have to spend $38.00
What segment is the projection of ST on QT?
UT
QU
QT
Answer:
UT
Step-by-step explanation:
The projection of ST on QT is found by locating the points on QT that are nearest the endpoints S and T of the original segment. On QT, U is the point closest to S, and T is the point closest to T. Then the projection is the segment between those identified points: UT.
Answer:
UT
Step-by-step explanation:
Help!
Assume that lines that appear tangent are tangent. Find the value of each variable.
It is so jard for me .
so by drawing construction i have done it.Value of x i haven't done.due to no perfect angle
Please help me out with this please
Intersecting Chord Theorem:
X = 1/2(78 + 76)
X = 1/2(154)
x = 77
A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6
Given:
A polynomial of the 5th degree A leading coefficient of 7A constant term of 6Problem-solving:
Let us prepare the leading terms, constant terms, and the coefficients of the polynomial are being asked.
[tex]\boxed{ \ 7x^5 + bx^4 + cx^3 + dx^2 + ex + 6 \ }[/tex]
Now we make the first polynomial, for example:
b = 3c = -2d = 2e = -5Thus, the result is [tex]\boxed{\boxed{ \ 7x^5 + 3x^4 - 2x^3 + 2x^2 - 5x + 6 \ }}[/tex]
Then we make the second polynomial as an alternative. For example:
b = -6c = 0d = -2e = 0Thus, the polynomial is [tex]\boxed{\boxed{ \ 7x^5 - 6x^4 + 4x^2 + 6 \ }}[/tex]
Of course, you can form another polynomial using the procedure above. Try to vary the coefficients.
Notes:
Let us rephrase the following definitions.
A monomial is an algebraic expression which comprises a single real number, or the product of a real number and one or more variables raised to whole number powers. For example, [tex]\boxed{-2} \boxed{3x^2} \boxed{4a^3b^4} \boxed{-5xy^3z^2} \boxed{\frac{3}{5}}[/tex]A coefficient is each real number preceeding the variable(s) in a monomial. In the examples above [tex]\boxed{ \ -2, 3, 4, -5, \frac{3}{5} \ }[/tex] are the coefficients.A polynomial is the sum or difference of a set of monomials. For example, [tex]\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }[/tex]Each monomial that forms a polynomial is called a term of that polynomial. For example, the term of polynomial [tex]\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }[/tex] are [tex]\boxed{ \ 2, - 3, and \ 4. \ }[/tex]The constant term is the term of polynomial that does not contain a variable.The leading coefficient is the coefficient of the term containing the variable raised to the highest power.For example, consider the polynomial [tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex]
[tex]\boxed{ \ 2x^4, - 3x^2, - 4x, and \ - 5 \ }[/tex] are the terms of polynomial.[tex]\boxed{ \ 2, - 3, - 4 \ }[/tex] are the coefficients.- 5 is the constant term.2 is the leading coefficient.A polynomial is said to be in standard form if the terms are written in descending order of degree. For example:
[tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex] is a polynomial in standard form.[tex]\boxed{ \ - 3x^2 + 2x^4 - 5- 4x \ }[/tex] is the polynomial, but it is not in standard form.Learn moreThe remainder theorem https://brainly.com/question/950038768.32 divided by 2.8 is divisible https://brainly.com/question/5022643#Determine whether each algebraic expression is a polynomial or not https://brainly.com/question/9184197#Keywords: a polynomial of the 5th degree, a leading coefficient of 7, a constant term of 6, a monomial, terms, the leading coefficient, constant, in a standard form, rational function, whole number power, integer
A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 could take the form of 'f(x) = 7x^5 + 6'. The other coefficients (b, c, d, e) can be any real numbers, but for simplicity, they can be set to zero in this instance.
Explanation:The student's question relates to constructing a polynomial of the 5th degree with specific characteristics in the field of Mathematics, specifically in algebra. One can present such a polynomial with the general form:
f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f
Where the leading coefficient a is 7 and the constant term f is 6. In this case, since the only information provided is the leading coefficient and the constant term, and not any constraints on the other coefficients (b, c, d, e), they can be any real numbers, including zero. Thus, one example of a polynomial fitting these constraints is:
f(x) = 7x^5 + 0x^4 + 0x^3 + 0x^2 + 0x + 6
To simplify the algebra and make calculations easier, one can eliminate terms wherever possible, which in this example has been executed by setting the coefficients of x^4, x^3, x^2, and x to zero. After forming any polynomial, it is also important to check the answer to ensure that it matches the given criteria, which in this case it does.
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The height of a triangle is 2 less than 5 times its base. If the base of the triangle is x feet, and the area of the triangle is 12 square feet, which equation models this situation?
A. 25x^2-10x-24=0
B. 5x^2-2x-24=0
C. 5x^2-2x-6=0
D. 5x^2-2x-12=0
Answer:
A. 5x^2 − 2x − 24 = 0
Step-by-step explanation:
height = 5b-2
b =x
We can rewrite the height as
h = 5x-2
We know the formula for area of a triangle
A = 1/2 bh
A =1/2 x * (5x-2)
Distributing the x
A= 1/2 (5x^2 - 2x)
We know A =12
12 = 1/2 (5x^2 - 2x)
Multiply each side by 2
12*2 = 2*1/2 (5x^2 - 2x)
24 = 5x^2 - 2x
Subtract 24 from each side
24-24 = 5x^2 - 2x-24
0 = 5x^2 - 2x-24
Which statements are true about a rectangular pyramid with a height of 9 centimeters and a base with the dimensions of 4 centimeters by 6 centimeters? Check all that apply.
A.The area of the base of the pyramid, B, is 8cm2.
B.The area of the base of the pyramid, B, is 24cm2.
C.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 3 times volume of this pyramid.
D.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 1/3 of the volume of this pyramid.
E.The volume of this pyramid is 72cm3.
F.The volume of this pyramid is 216cm3.
Answer:
B.The area of the base of the pyramid is 24cm^2.
C.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 3 times volume of this pyramid.
E.The volume of this pyramid is 72cm3.
Step-by-step explanation:
Area of base of the pyramid = l × w = 4 × 6 = 24 cm^2
Volume of rectangular pyramid = (l × w × h)/3 = (4 × 6 × 9)/3 = 72 cm^3
Volume of rectangular prism = w × h × l = 9 × 4 × 6 = 216 cm^3
So according to these calculations, the correct answer options are:
B.The area of the base of the pyramid is 24cm^2.
C.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 3 times volume of this pyramid.
E.The volume of this pyramid is 72cm3.
Final answer:
The true statements about the rectangular pyramid are B, C, and E.
The base area is 24 cm² (Statement B), the volume of the pyramid is 72 cm³ (Statement E), and the volume of a similarly dimensioned rectangular prism is three times that of the pyramid (Statement C).
Explanation:
To determine which statements are true about the rectangular pyramid with given dimensions, we need to calculate the base area and the volume of both the pyramid and the rectangular prism and compare them.
The base area of the pyramid, denoted as B, is the area of the rectangle formed by the base's dimensions.
Therefore, B = length x width = 4 cm x 6 cm = 24 cm².
Thus, statement B is true.
For the volume of the pyramid (V), we use the formula V = (1/3) x B x height.
Plugging the values, we get V = (1/3) x 24 cm² x 9 cm, which equals 72 cm³.
So, statement E is true.
The volume of a rectangular prism with the same height and base dimensions is volume of the prism = length x width x height = 4 cm x 6 cm x 9 cm = 216 cm³.
Since the volume of the prism is three times the volume of the pyramid, statement C is true.
Statements A, D, and F are not true based on the above calculations and explanations.
A sample proportion of 0.18 is found. To determine the margin of error for this statistic, a simulation of 100 trials is run, each with a sample size of 50 and a point estimate of 0.18.
The minimum sample proportion from the simulation is 0.28, and the maximum sample proportion from the simulation is 0.40.
What is the margin of error of the population proportion using an estimate of the standard deviation?
A) ±0.02
B) ±0.04
C) ±0.12
D) ±0.18
Answer:
The answer is B. 0.04
Step-by-step explanation:
too lazy to write
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?
a. (–3, –0.90)
b. (–2.5, –0.75)
c.(4.5, 1.35)
d. (8, 2.40)
Answer:
The correct answer would be (8,2.40).
Step-by-step explanation:
Option one(-3, -0.9) and two (-2.5, -0.75) Would not be a viable solution because the value of number of days can not be negative and in option one and two, value of days -3 and -2.5 is negative.
Option three(4.5, 1.35) can not be correct because library charges fee for a full day so the number for days would be a whole number. Library would not charge for 4.5 days, they would either charge of 4 days or 5 days because 4.5 is not an whole number.
Option four(8, 2.40) is the correct answer because it satisfies our equation;
Y= 0.30 * X
2.40= 0.30 * 8
2.40 = 2.40
hope this helps :)
D is the right answer
The ShowMe Theater is showing 12 movies. Each movie is shown at five different times during during the day. How many choices of movies and showtime does Bart have?
bart has a choice of twelve different movies at 5 different times each so you just multiply twelve and five to get 60 choices
Answer:
Bart has 60 choices.Step-by-step explanation:
Givens
The theater is showing 12 movies.Each movie is shown at five different times.To find the total number of choices of movies and showtime that Bart have, we just need to multiply. Because, if each movie is shown at five different times, and there are 12 movies, then the total number of choices are
[tex]12 \times 5 = 60[/tex]
Therefore, Bart has 60 choices to watch a movie.
A light bulb operates at a voltage of 110 volts and consumes 50 watts of power. How much current flows through the light bulb?
Answer:
5/11 amperes ≈ 0.455 amperes
Step-by-step explanation:
The applicable formula for the current (I) is ...
I = P/V . . . . where P is power in watts, and V is voltage in volts
I = (50 watts)/(110 volts) = 5/11 amperes
What shape is the cross-section of the cylinder hone sliced perpendicular to its base?
A. Circle
B. Rectangle
C. Square
D. Triangle
Answer:
circle should be the answer
The answer is A. Circle
What is x? Help please
Answer: [tex]x=\frac{8}{3}[/tex]
Step-by-step explanation:
By the Intersecting secants theorem, we know that:
[tex]EC*ED=EB*EA[/tex]
Then, substituting, we get:
[tex](x+4)(x+4+1)=(x+1)(x+1+11)\\\\(x+4)(x+5)=(x+1)(x+12)[/tex]
Now we need to expand the expression:
[tex]x^2+5x+4x+20=x^2+12x+x+12[/tex]
Simplifying, we get that the value of "x" is:
[tex]x^2+9x+20=x^2+12x+12\\\\9x+20=12x+12\\\\20-12=12x-9x\\\\8=3x\\\\x=\frac{8}{3}[/tex]
Please help me out please
By comparing the perimeters, we can deduce the scaling factor:
[tex]k = \dfrac{34}{20} = 1.7[/tex]
The areas scale with the square of the scaling factor, so the new area is
[tex]19.6 \cdot 1.7^2 = 56.644[/tex]
If g(x)=f(x+1), then g(x) translates the function f(x) 1 unit _[blank]_.
Left
Right
Up
Down
answer: right
reason: because you are talking about the x axis so if you go left that would be a negative and you cant go up and down bc that's the y axis so the only way to go is right
hope this helped
PLEASE HELP ASAP 50 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
3x^3 and 2x^3 should be combined because if numbers have an exponent combine only if they both have matching exponents and variables as well
Hope this helped!
~Just a girl in love with Shawn Mendes
A card is drawn from a standard deck and a letter chosen from the word INCREDIBLE. What is the probability of drawing a king then getting an I
Answer:
2/10 simplify into 1/5
Step-by-step explanation:
Since there is a total of 10 cards in the deck, the denominator would be 10. As there is only two 'I's in the deck it would be the numerator.
Hope this will help :)
Answer:
2/130 = 1/65
Step-by-step explanation:
There are 4 kings out of 52 cards total. Your chances of drawing a king are 4/52
Incredible has 10 letters 2 of which are 'i's' So your chances of picking 2 eyes is 2/10
Combined you have
4/52 * 2/10 = 2/ 130 = 1/65
Please please help me
Answer:
131 m³
Step-by-step explanation:
The volume (V) of a cone is
V = [tex]\frac{1}{3}[/tex] area of base × height
= [tex]\frac{1}{3}[/tex] × π × 5² × 5
= [tex]\frac{1}{3}[/tex] π × 125 ≈ 131
Please answer this question CORRECTLY for 30 points and brainliest!
Answer:
22 quarters
Hope this helps! Correct me if im wrong.
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square 20? Also find the total number of grains of wheat on the board at this time and their total weight
Answer:
See below in bold.
Step-by-step explanation:
Here is 1 grain on square 1 , 2 on square 2, 4 on square 3 and so on. This is a geometric sequence with the nth term = a1r^(n - 1) where a1 = first term , r = common ratio.
So the 20th term (the number of grains on square 20) would be
1*2^(20-1) = 524,288.
Total = a1 * (r^n - 1) / (r - 1)
= (2^20 - 1) / 2-1 = 1.048,575
a small coin is thrown off the eiffel tower in paris. It lands 62.5m away from the centre of the base of the 320m- high structure. find the angle of elevation from the coin to the top of the tower
Answer:
78.9 degrees to the nearest tenth.
Step-by-step explanation:
This equals the angle whose tangent is 320/62.5 ( opposite side / adjacent side).
The angle of elevation from the coin to the top of the tower
What is angle of elevation?
The angle formed by the line of sight and the horizontal plane for an object above the horizontal.
Given that:
The coin lands 62.5m away from the center of the base of the 320m- high structure.
Height= 320 m
Base= 62.5 m
Now, tan [tex]\theta[/tex] = [tex]\frac{P}{B}[/tex]
=[tex]\frac{320}{62.5}[/tex]
= 5.12
[tex]\theta[/tex]= [tex]tan^{-1} (5.12)[/tex]
[tex]\theta[/tex]= [tex]78.94^{0}[/tex]
The angle of elevation is: 78.94 degrees.
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F(x) = 3x-1 and g(x)=2x^2
a. Find (f g) (x).
b. Find (f-g) (x).
c. Find f(g(x)).
d. Find g(f(x)).
Answer:
See below
Step-by-step explanation:
a. here you are to multiply the two functions together:
[tex](3x-1)(2x^{2} )=6x^{3}-2x^{2}[/tex]
b. here you are to subtract g from f:
[tex](3x-1)-(2x^{2})=-2x^{2}+3x-1[/tex]
c. here you are to compose g into f. In other words, pick up the whole g function and plug it into f wherever you see an x:
[tex]3(2x^{2} )-1=6x^{2} -1[/tex]
d. here you are compose f into g. In other words, pick up the whole f function and plug it into g wherever you see an x:
[tex]2(3x-1)^2[/tex]
You now have to FOIL out the (3x-1) like so:
[tex]2[(3x-1)(3x-1)][/tex]
which gives you
[tex]2(9x^{2} -6x+1)[/tex]
Distribute in the 2 and you'll end up with the answer:
[tex]18x^{2} -12x+2[/tex]
Find the direction of vector u shown
[tex]\vec u[/tex] starts at (1, 1) and ends at (-4, 3), so it's pointing in the same direction as the vector
[tex](-4, 3)-(1,1)=(-5,2)[/tex]
This vector terminates in the second quadrant, so its direction is
[tex]\pi+\tan^{-1}\left(-\dfrac25\right)\,\mathrm{rad}\approx158.2^\circ=(180-158.2)^\circ\,\text{N of W}=21.8^\circ\text{N of W}[/tex]
Answer:
C. 21.8 degrees N of W
Step-by-step explanation:
got it right on edge :)
Find the 7th term of the expansion of (3c + 2d)^9.
a.
760c^3d^6
c.
145,152c^3d^6
b.
760c^4d^5
d.
145,152c^4d^5
Answer:
c
Step-by-step explanation:
Using Pascal's triangle, the expansion, although EXTREMELY lengthy, will help you find the 7th term. I am going to type out the expansion only up til the 7th term (although there are actually 10 terms because we are raised to the power of 9). If you would like to learn how to use Pascal's Triangle for binomial expansion, you will need to visit a good website that explains it because it's just too difficult to do it via this website.
The expasion is as follows (up to the 7th term):
[tex]1(3c)^{9} +9(3c)^{8}(2d)^{1} +36(3c)^{7}(2d)^{2} +84(3c)^6(2d)^3+126(3c)^5(2d)^4+126(3c)^4(2d)^5+84(3c)^3(2d)^6[/tex]
That last term is the 7th term. You find out its value by multiplying all the numbers together and adding on the c^3d^6. Again those come from Pascal's triangle, and it's one of the coolest math things ever. I encourage you to take the time to explore how it works.
what was the total amount of all checks vera deposited
Answer:
(d) $1120.70
Step-by-step explanation:
You want the total of deposited checks as shown on the deposit slip.
TotalThe total value of checks is shown on the line "Subtotal." This is amount of the deposited checks. The same deposit slip shows a withdrawal of $80 cash, so the net deposit is $80 less than that subtotal.
Vera deposited $1120.70 in checks, choice D.
The correct total amount of all checks Vera deposited is $664.30, and the deposit ticket reflects a subtotal of $1040.70, which includes both checks and cash. Therefore, option (b) $664.30 is the accurate representation of the total amount of all checks.
To determine the total amount of all checks Vera deposited, we need to add the amounts of the individual checks listed on the deposit ticket.
1. Check #184: $138.09
2. Check #308: $312.15
3. Check #298: $214.14
Adding these amounts: $138.09 + $312.15 + $214.14 = $664.38
Therefore, the correct answer is option (b) $664.30. This represents the total amount of all checks Vera deposited. The deposit ticket indicates the subtotal of checks as $1120.70, but this includes the cash amount received as well. To find the total amount of all checks, we subtract the cash amount received, which is $80.00, from the subtotal: $1120.70 - $80.00 = $1040.70.