The probability of Aminata choosing a specific type of fruit is calculated by dividing the number of that fruit by the total number of fruits in the bowl. Different fruit types have different probabilities due to their varying quantities.
Explanation:The question asks about the probability of Aminata choosing a specific type of fruit from a bowl containing 3 apples, 4 bananas, 2 pears, and 1 orange. To find the probability of Aminata choosing any one type of fruit, we first need to determine the total number of fruit pieces in the bowl, which is 3 apples + 4 bananas + 2 pears + 1 orange = 10 pieces of fruit.
The probability of selecting any specific type of fruit is then calculated by dividing the number of that fruit type by the total number of pieces.
The probability of choosing an apple is 3/10.The probability of choosing a banana is 4/10 or simplified to 2/5.The probability of choosing a pear is 2/10 or simplified to 1/5.The probability of choosing an orange is 1/10.Each fruit type has a different probability of being chosen based on its quantity in the total mix of fruits.
How do u do question 27 and 29. Find the measure of angle x?
Will mark brainliest and give 20 points!
What is the quotient of 8,688 ÷ 24?
362
434
450
8,664
The front side of a playhouse is shown in this scale drawing. The height of the door in the drawing 1.8 inches. The scale that maps the drawing to the actual playhouse is 1 inch to 2.5 feet.
Final answer:
To find the actual height of a door in a playhouse from a scale drawing with a scale of 1 inch to 2.5 feet, simply multiply the drawing measurement (1.8 inches) by the scale factor, which gives an actual height of 4.5 feet.
Explanation:
To determine the actual height of the door on the playhouse from the scale drawing, you need to use the provided scale ratio, which is 1 inch to 2.5 feet.
Since the height of the door in the drawing is 1.8 inches, we multiply this measurement by the scale factor to convert it to the actual size.
Calculation: 1.8 inches × 2.5 feet/inch results in an actual door height of 4.5 feet on the actual playhouse.
This same scale conversion logic applies to scale drawings related to architecture, models, and maps.
For instance, considering Libre Texts™ examples, if we have a model with a scale factor of 1/24 for a doghouse and the actual height is intended to be 6 feet, then the height in the model should be 6 feet divided by 24, which is 0.25 feet or 3 inches. Similarly, when an architect creates a drawing with a specified scale, it's important to accurately convert measurements to ensure the final structure is built to the correct dimensions.
How do you know a radical expression is in simplest form?
What is the slope of the line that passes through the points E(3, 0) and F (6, -3)?
Hello!
Step-by-step explanation:
Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]
[tex]\frac{(-3)-0=-3}{6-3=3}=\frac{-3}{3}=-1[/tex]
Therefore, the slope is -1.
Answer is -1.
Hope this helps!
Thanks!
-Charlie
Have a great day!
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please help I will mark brainlist if correct
A rental car costs a one time fee of $150 and then an additional $80 for each day it is rented. If the Nawa family's total bill was $470, how many days did they rent the car?
Nawa family rented the car for 2 days.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
A rental automobile costs $150 for the first day and an extra $80 for each consecutive day booked. If the entire bill for the Nawas family was $470.
The total cost of the rental car per day is :
⇒ one-time fee + additional fee
⇒ $150 + $80
Apply the addition operation,
⇒ $230 per day.
The Nawas paid $470 for the rental car, so they rented the car for $470 / $230 per day = 2 days.
Therefore, his family rented the car for 2 days.
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The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring. What is the constant of the quadratic function in this equation?
(a - b)(a 2 + ab + b 2) HELP
The area of a rug, which is shaped like a rectangle,is 4x²+4x square feet. Factor this polynomial to find expressions for the dimensions of the rug
Final answer:
The expressions for the dimensions of a rectangular rug with an area of 4x²+4x square feet are 4x feet and (x + 1) feet after factoring the polynomial.
Explanation:
To find the expressions for the dimensions of the rug with an area of 4x²+4x square feet, we need to factor the polynomial. Factoring out the greatest common factor (GCF), we get:
4x² + 4x = 4x(x + 1).
This indicates that one dimension of the rug is 4x feet and the other dimension is (x + 1) feet. The rug can be visualized as a rectangle where one side is 4 times a certain length x, and the other side is that length plus one.
Which graph is defined by f(x) = |x2 − x − 2|?
In what ways do you think presidents today are more powerful than they were in the past?
Modern presidents are more powerful than their predecessors due to access to advanced technologies, executive actions, and media influence.
Explanation:Presidents today are more powerful than they were in the past due to various factors. Firstly, modern presidents have access to advanced technologies such as television, the internet, and social media, which allow them to shape public opinion and build support for their policies. Secondly, they have a greater ability to use executive action, including executive orders and signing statements, to bypass Congress and enact their own policies. Finally, modern presidents can use their popularity and media attention to increase pressure on Congress and influence policy change.
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Tom separated the rectangle shown below into 8 equal parts what fraction shows the area of one of the parts
Tom divided the rectangle into 8 equal parts, and each part represents 1/8 of the total area. This fraction is derived from the fact that division of an area into equal parts means each part is one of those parts as a fraction of the whole.
Tom divided the rectangle into 8 equal parts. If we are to find the fraction that represents the area of one of these parts, we simply consider that each part should be an equal division of the whole. Hence, one part out of eight equal parts is represented by the fraction 1/8. This is because division by 8 is equivalent to multiplication by its reciprocal, which is 1/8. This is the same as dividing the rectangle into smaller, more manageable areas, such as rectangles, and determining the area of one such rectangular area.
It's important to understand that in a rectangle divided evenly into parts, any single part represents a fraction of the whole, with the denominator reflecting the total number of parts. In this case, since there are 8 parts, each individual part is 1/8 of the total area. This provides us with a simple way to address problems involving finding fractions of areas, particularly when the total area is partitioned into equally-sized segments.
Which of the ollowing statements best describes he relationship between a line and a point in a plane
if you were to solve the following system by substitution what would be the best variable to solve and from what equation? 2x+8y=12 3x-8y=11
Answer:
X in 1st
Step-by-step explanation:
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 10 child bikes and 12 adult bikes in the week. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
The Correct answer is Option C) is correct: "Yes, because the bike order meets the restrictions of [tex]4c+6a\leq 120[/tex] and [tex]4c+4a\leq 100[/tex]."
To determine whether the company can build [tex]10[/tex] child bikes (c) and [tex]12[/tex]adult bikes (a) within the given time constraints, we need to check if the total building time and testing time for both types of bikes do not exceed the limits.
Each child bike requires [tex]4[/tex] hours to build and [tex]4[/tex] hours to test, while each adult bike requires [tex]6[/tex] hours to build and [tex]4[/tex] hours to test.
So, the total building time [tex](4c+6a)[/tex] and the total testing time [tex](4c+4a)[/tex]for the given number of bikes should not exceed the maximum limits of [tex]120[/tex] hours and [tex]100[/tex] hours, respectively.
Therefore, the system of inequalities that best represents this scenario is:
[tex]4c+6a\leq 120\\4c+4a\leq 100[/tex]
Option 3) is correct: "Yes, because the bike order meets the restrictions of [tex]4c+6a\leq 120[/tex] and [tex]4c+4a\leq 100[/tex]."
COMPLETE QUESTION:
A bicycle manufacturing company makes a particular type of bike. Each child bike requires [tex]4[/tex] hours to build and [tex]4[/tex] hours to test. Each adult bike requires [tex]6[/tex] hours to build and [tex]4[/tex] hours to test. With the number of workers, the company is able to have up to [tex]120[/tex] hours of building time and [tex]100[/tex] hours of testing time for a week. If [tex]c[/tex] represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build [tex]10[/tex] child bikes and [tex]12[/tex] adult bikes in the week.
A) No, because the bike order does not meet the restrictions of [tex]4c + 6a \leq 120[/tex] and [tex]4c + 4a \leq 100[/tex]
B) No, because the bike order does not meet the restrictions of [tex]4c + 4a \leq 120[/tex] and [tex]6c + 4a \leq 100[/tex]
C) Yes, because the bike order meets the restrictions of [tex]4c + 6a \leq 120[/tex]and [tex]4c + 4a \leq 100[/tex]
D) Yes, because the bike order meets the restrictions of [tex]4c + 4a \leq 120[/tex]and [tex]6c + 4a \leq 100[/tex]
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Arnold borrowed $7890 at 11.5 percent for five years. How much did Arnold Pay in interest?
A.$2,199
B.$2,300
C.$1,150
D.$2.520
Answer:
Option D. $2520 is correct
Step-by-step explanation:
Principal value = $7890
Rate of interest = 11.5 annually
[tex]\text{Monthly Rate of Interest = }\frac{11.5}{12}=0.96\%=0.0096[/tex]
Time = 5 years
⇒ n = 60 months
[tex]\text{Monthly Payment = }\frac{rate\times \text{Principal value}}{1-(1+r)^{-n}}\\\\\text{Monthly payment = }\frac{0.0096\times 7890}{1-(1+0.0096)^{-60}} \\\\\implies\text{Monthly Payment = }\$173.50[/tex]
Total payment made by Arnold = No. of months × Monthly Payment
⇒ Total Payment = 60 × 173.50
⇒ Total Payment = $10410
Money borrowed = $7890
Hence, Amount of interest = Total payment - Amount borrowed
⇒ Interest = 10410 - 7890
⇒ Interest = $2520
Therefore, Option D. $2520 is correct
Please help!!! Fast
Which is a solution of x2 – x – = 0?
[tex]x^2-x=0\\\\x(x-1)=0\iff x=0\ \vee\ x-1=0\\\\\boxed{x=0\ \vee\ x=1}[/tex]
The simple interest on a principal amount, P, borrowed for T years at R% annual interest is given by the following formula. Which of the following describes the relationship between the variables of the simple interest formula?
1.P depends on R and T
2.R depends on P and T
3.I depends on P, R, and T
4.R depends on I
Answer:
3. I depends on P, R, and T.
Step-by-step explanation:
We have been given the simple interest formula [tex]I=PRT[/tex], where,
I = Amount of simple interest,
P = Principal amount,
T = Time in years,
R= Interest rate.
The bigger principal amount and higher interest rate for a long period of time will result in big amount of interest, while small principal amount at a smaller interest rate and for a small period of time will result in small amount of interest.
Since amount of interest depends on principal amount, rate and time, therefore, 3rd option is the correct choice.
Two examples of items the weigh less than an ounce
Janet has three times as many dimes as nickels and twice as many quarters as nickels. If she has $3.40 in all, how many nickels, dimes, and quarters does she have?
If n represents the number of nickels Janet has, which of the following equations could be used to solve the problem?
5n + 10n + 25n = 340
n + 3n + 2n = 340
5n + 30n + 50n = 340
Answer:
[tex]5n+30n+50n= 340[/tex]
Step-by-step explanation:
Janet has three times as many dimes as nickels and twice as many quarters as nickels.she has $3.40 in a.
Let n be the number of nickels
d be the number of dimes and q be the number of quarts
1 nickel = 5 cents
1 dime = 10 cents
1 quarter = 25 cents
Convert the dollars into cents by multiplying by 100
3.40 dollars = 3.40 times 100 is 340 cents
Janet has three times as many dimes as nickels and twice as many quarters as nickels
dimes is 3 times of nickels
[tex]d=3n[/tex]
quarts is twice as many as nickels
[tex]q=2n[/tex]
Now we frame equation
5 nickels plus 10 dimes plus 25 quarts is total 340 cents
[tex]5n+10d+25q= 340[/tex]
Replace d and q
[tex]5n+10(3n)+25(2n)= 340[/tex]
[tex]5n+30n+50n= 340[/tex]
Evaluate the expression 14.3 minus 2 times 5 to the 2nd power divided by 5
Answer:
4.3
Step-by-step explanation:
We are given that an expression
[tex]14.3-2\times 5^2\div 5[/tex]
We have to find the value of given expression.
DMAS rule:
D=Divided first
M=Multiply
A=Addition
S=Subtraction
Using DMAS rule ,
We solve first divide operation
[tex]14.3-2\times 5^{2-1}[/tex]
Using property: [tex]a^x\div a^y=a^{x-y}[/tex]
Then, we get
[tex]14.3-2\times 5[/tex]
Now, we solve multiply operation
[tex]14.3-10[/tex]
Now, we solve subtraction operation
[tex]4.3[/tex]
Hence, [tex]14.3-2\times 5^2\div 5=4.3[/tex]
The center of a circle is at (−3, 1) and its radius is 9.
What is the equation of the circle?
(x+3)2+(y−1)2=18
(x−3)2+(y+1)2=18
(x−3)2+(y+1)2=81
(x+3)2+(y−1)2=81
The standard form of the circle equation is in the form [tex] (x-h)^{2}+(y-k)^{2}=r^{2} [/tex] with the center being at the point [tex] (h,k) [/tex] and the radius being "r".
We have to find the equation of circle with center (-3,1) and radius as 9.
So, h= -3, k=1 and r=9
Equation of circle is:
[tex] (x-(-3))^{2}+(y-1)^{2}=(9)^{2} [/tex]
[tex] (x+3)^{2}+(y-1)^{2}=81 [/tex] is the required equation of the circle.
Therefore, Option 4 is the correct answer.
if dy/dx= sin x/ cos y and y(0) = 3pi/2, find an equation for y in terms of x
Final answer:
The problem requires finding an equation for y in terms of x given a differential equation and an initial condition. Solving for y, we get:[tex]\[ y = \arcsin(-\cos(x)) \][/tex]
This is the equation for y in terms of x.
Explanation:
To solve this ordinary differential equation (ODE), we can separate variables and then integrate both sides. Given:
[tex]\[\frac{dy}{dx} = \frac{\sin(x)}{\cos(y)}\][/tex]
We separate variables by multiplying both sides by \(dx\) and dividing by Cos(y) to isolate y terms:
[tex]\[\cos(y) \, dy = \sin(x) \, dx\][/tex]
Now, we integrate both sides. For the left side, we integrate with respect to y, and for the right side, we integrate with respect to x:
[tex]\[\int \cos(y) \, dy = \int \sin(x) \, dx\][/tex]
Integrating each side gives us:
[tex]\[ \sin(y) = -\cos(x) + C\][/tex]
Where C is the constant of integration.
Given the initial condition [tex]\(y(0) = \frac{3\pi}{2}\)[/tex], we can plug this into the equation to find [tex]\(C\):[/tex]
[tex]\[ \sin\left(\frac{3\pi}{2}\right) = -\cos(0) + C \][/tex]
[tex]\[ -1 = -1 + C \][/tex]
[tex]\[ C = 0 \][/tex]
So the equation becomes:
[tex]\[ \sin(y) = -\cos(x) \][/tex]
Therefore, solving for y, we get:
[tex]\[ y = \arcsin(-\cos(x)) \][/tex]
This is the equation for y in terms of x.
Which is an equation of the line graphed below?
A. y=2x-3
B. y=1/2x-3
C. y= -1/2x-3
D. y= -2x-3
54 points
BC is parallel to DE. What is the length of CE? A) 2 1/3 B) 2 2/3 C) 3 1/3 D) 3
Answer:
2 2/3
Step-by-step explanation:
AB
BD
=
AC
CE
3 /2 = 4 /CE → CE = 8 /3 = 2 2 /3
Factor completely. x2−12x+35 Enter your answer in the box.
The complete factor of x² − 12x + 35 is (x - 7(x - 5).
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would factor completely the quadratic function x² −12x+35 by using the factorization method as follows;
x² − 12x + 35 = 0
x² − 7x - 5x + 35 = 0
x(x - 7) - 5(x - 7) = 0
(x - 7(x - 5) = 0.
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Complete Question:
Factor completely. x² −12x+35 Enter your answer in the box.
The school store started selling music CDs five years ago. They sold $22,600 worth in the first year. But, since MP3 players became so popular, the total yearly sales of CDs have dropped 14% per year since then. What is the total money collected for music CDs sold in the school store over the last five years? Use the geometric series formula to calculate your answer.
The total money collected for music CDs sold in the school store over the last five year is $85,557
Geometric Series Formula:
To calculate the total money collected for music CDs sold in the school store over the last five years, we can use the formula for the sum of a geometric series: Sum = a * (1 - r^n) / (1 - r), where a is the initial value, r is the common ratio, and n is the number of terms.
Given Data:
Initial sales in the first year = $22,600
Annual decrease rate = 14%
Duration = 5 years
Calculation Steps:
Calculate the common ratio: r = 1 - 0.14 = 0.86
Plug the values into the formula: Sum = $22,600 * (1 - 0.86^5) / (1 - 0.86) = $85,557