Final answer:
Eve should knit between 3 and 6 scarves each day for the remaining 2 days to meet her goal of knitting at least 15 and at most 21 scarves for the week. The inequality that represents this situation is 3 \<= x \<= 6.
Explanation:
Eve has knitted 9 scarves and wants to knit at least 15 and at most 21 scarves for the week. With 2 days of the workweek left, we need to find out how many scarves she should knit each day to meet her goal. Let's denote x as the number of scarves Eve knits each day for the next two days.
Since Eve has already knitted 9 scarves and wants to knit at least 15, the minimum number of additional scarves she needs to knit is 15 - 9 = 6. So, in 2 days, she must knit at least 6 scarves. This gives us the inequality 2x ≥ 6.
Similarly, the maximum number of scarves Eve aims to knit is 21. Therefore, the maximum number of additional scarves she can knit is 21 - 9 = 12. This leads us to the inequality 2x ≤ 12.
Combining both inequalities, we get 3 ≤ x ≤ 6, which tells us that Eve needs to knit between 3 and 6 scarves each day to meet her goal.
Solve the system of equations algebraically.
*If necessary, write your answers as fractions in simplest form.
y = x + 2
y = -3x
Answer:
Step-by-step explanation:
y = x + 2 -------------(i)
y = -3x ----------------(ii)
substitute y = -3x i equation (i)
-3x = x + 2
-3x -x = 2
-4x = 2
x = 2/-4
x = -1/2
Substitute x = -1/2 in (ii)
y = -3 * -1/2
y = 3/2
The savings rate for two students is shown.
Fill in the blanks to correctly compare the two students account
Anna opens her savings account with $_______ less than Alec used to open his account. Anna adds $_______ more per week to her account than Alec adds to his.
Answer:
2 less
3 more
Step-by-step explanation:
brainliest please
Anna opens her savings account with 'Y' dollars less than Alec's initial account amount, and she adds 'W' dollars more to her account each week compared to Alec.
Explanation:Given that we want to compare the savings accounts of two students, Anna and Alec, let's assume that Alec opens his savings account with 'X' amount of dollars, and Anna opens hers with 'Y' amounts less than Alec, making her initial amount 'X-Y' dollars. Additionally, if Alec adds 'Z' dollars per week to his account, but Anna adds 'W' dollars more than Alec each week, Anna would be adding 'Z+W' dollars to her account weekly.
So, to fill in the blanks, you could say: Anna opens her savings account with 'Y' less than Alec used to open his account. Anna adds 'W' more per week to her account than Alec adds to his. By comparing this way, we can look at the differences in both the initial investment and the weekly contributions for each of the students' savings accounts.
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At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .51.
Find the probability that in a sample of 10 customers, at least 7 will order a nonalcoholic beverage.
Answer:
[tex]P(x\geq 7)=0.1886[/tex]
Step-by-step explanation:
The variable x, that said the number of customer that will order a nonalcoholic beverage in a sample of n customers follows a binomial distribution. Because we have n identical and independent events with a probability p of success and (1-p) of fail.
So, the probability that x customers will order a nonalcoholic beverage is:
[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]
Where n is the size of the sample and p is the probability that a customer order a nonalcoholic beverage, so replacing the values, we get:
[tex]P(x)=\frac{10!}{x!(10-x)!}*0.51^{x}*(1-0.51)^{10-x}[/tex]
Now, the probability that at least 7 will order a nonalcoholic beverage is equal to:
[tex]P(x\geq 7)=P(7)+P(8)+P(9)+P(10)[/tex]
Where:
[tex]P(7)=\frac{10!}{7!(10-7)!}*0.51^{7}*(1-0.51)^{10-7}=0.1267\\P(8)=\frac{10!}{8!(10-8)!}*0.51^{8}*(1-0.51)^{10-8}=0.0494\\P(9)=\frac{10!}{9!(10-9)!}*0.51^{9}*(1-0.51)^{10-9}=0.0114\\P(10)=\frac{10!}{10!(10-10)!}*0.51^{10}*(1-0.51)^{10-10}=0.0011[/tex]
So, [tex]P(x\geq 7)[/tex] is equal to:
[tex]P(x\geq 7)=0.1267+0.0494+0.0114+0.0011\\P(x\geq 7)=0.1886[/tex]
Finally, the probability that in a sample of 10 customers, at least 7 will order a nonalcoholic beverage is equal to 0.1886
El perímetro del cuadrado ABCD es 24cm. Halla la medida de
forma simple:
Answer:
Sides: 6 cms
Diagonal: 8.49 cms
Step-by-step explanation:
In a square the possible measurements to calculate are its sides and its diagonal, therefore we calculate both:
The perimeter of a square is calculated as the sum of its four sides. This is defined as a figure that has four equal sides, then:
4/24 = 6
Therefore each side measures 6 cm.
For the diagonal, we use pythagoras since it corresponds to the hypotenuse of a right triangle that is formed by drawing the diagonal:
c ^ 2 = a ^ 2 + b ^ 2
c ^ 2 = 6 ^ 2 + 6 ^ 2
c ^ 2 = 36 + 36 = 72
c = 72 ^ (1/2)
c = 8.49
What the diagonal means is 8.49 cm.
A marathon is 26.2 miles. What is the least number of times Miguel must run for his total distance run during training to exceed the distance of a marathon?
Missing part of the question
Miguel has started training for a race. The first time he trains, he runs 0.5 mile. Each subsequent time he trains, he runs 0.2 mile farther than he did the previous time.
What is the arithmetic series that represents the total distance Miguel has run after he has trained n times?
Answer:
The least number of times Miguel must run for his total distance run during training to exceed the distance of a marathon is 17.3 miles
Step-by-step explanation:.
Given parameters
Miguel first run = 0.5 mile
Subsequent run = 0.2 mile
This question is an arithmetic progression.
We'll make use of arithmetic progression formula to solve this
Formula:.
Tn = a + (n - 1)d
Where a = first term
n = number of terms
d = common difference
In this case
a = first run = 0.5 mile
d = subsequent run = 0.2 mile
So, Tn = a + (n - 1)d become
Tn = 0.5 + (n - 1) 0.2
Tn = 0.5 + 0.2n - 0.2
Tn = 0.5 - 0.2 + 0.2n
Tn = 0.3 + 0.2n
The arithmetic series of an arithmetic progression is calculated using
Sn = ½(a + Tn) * n
By substituton, we have
Sn = ½(0.5 + 0.3 + 0.2n) * n
Sn = ½(0.8 + 0.2n) * n
Sn = 0.4n + 0.1n²
b.
Since the race is 26.2 miles then the least number of times is given as
Sn ≥ 26
0.4n + 0.1n² ≥ 26.2
0.1n² + 0.4n - 26.2 ≥ 0
Using quadratic formula
n = (-b ± √(b² - 4ac))/2a
Where b = 0.4 a = 0.1 and C = -26.2
So,
n = -0.4 ± √(0.4² - 4 * 0.1 * ,26.2)/2 * 0.1
n = (-0.4 ± √10.64)/0.2
n = (0.4 ± 3.26)/0.2
n = (0.4 + 3.26)/0.2 or (0.4 - 3.26)/0.2
n = 3.46/0.2 or -2.86/0.2
n = 17.3 or -14.3
Since n can't be negative
n = 17.3 miles
The least number of times Miguel must run for his total distance run during training to exceed the distance of a marathon is 17.3 miles
Answer:
15 times
Step-by-step explanation:
What is the area of this composite figure?
A figure is comprised of 2 rectangles. The rectangles are 10 feet by 6 feet, and 10 feet by 4 feet.
A. 12 feet squared
B. 80 feet squared
C. 88 feet squared
D. 100 feet squared
Answer:
The answer would be 88 ft squared
Step-by-step explanation:
If you make the shape into a rectangle it would be 100 and then subtract the amount that isn't filled in it would be 88.
The required area of the composite figure is 100 feet squared. The correct answer is option D.
What is surface area?
The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
To find the area of the composite figure, we need to add up the areas of the two rectangles.
The first rectangle has dimensions of 10 feet by 6 feet, so its area is:
10 ft × 6 ft = 60 ft²
The second rectangle has dimensions of 10 feet by 4 feet, so its area is:
10 ft × 4 ft = 40 ft²
The total area of the composite figure is:
60 ft² + 40 ft^2 = 100 ft²
Thus, the area of the composite figure is 100 feet squared. The correct answer is option D.
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3. There is 1/4 of an apple in every container of fruit. Show the number of apples in 5 containers
using a fraction.
Answer:
Answer:
Step-by-step explanation:
Instead, you will use diagrams. To solve such a problem, you must produce a diagram which clearly shows all of the fractions involved in the ... between them have eaten five of the pieces, they have eaten 5/6 of the cake. We also see that ... counting numbers with M<N), then you must show the thing, show it clearly.
Which type of transformation would move figure 1 onto
figure 2?
translation
reflection,
rotation
dilation
Answer:
reflection
Step-by-step explanation:
skraight up homie.
The type of transformation would move figure 1 onto figure 2 is Dilation.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
As, from the figures
Figures 1 and 2 can be properly observed to reveal that they have similar shapes to one another.
Accordingly, figure 1 is a bigger version of figure 2, and vice versa.
As a result, dilation and specifically enlargement is the transformation employed to convert figure 2 to figure 1.
Hence, the transformation is Dilation.
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Blake drew a circle with a circumference of 37.68 cm. What is the diameter of that circle?
Given Information:
Circumference of circle = C = 37.68 cm
Required Information:
Diameter of circle = D = ?
Answer:
Diameter of circle = [tex]D = 11.99[/tex] [tex]cm[/tex]
Step-by-step explanation:
We know that circumference of a circle is given by
[tex]C=2\pi r[/tex]
Where r is the radius of circle.
The relation between radius and diameter is given by
[tex]r = \frac{D}{2}[/tex]
Substitute r into above equation of circumference.
[tex]C=2\pi (\frac{D}{2} )[/tex]
[tex]C=\pi D[/tex]
[tex]D = \frac{C}{\pi}[/tex]
[tex]D = \frac{37.68}{\pi}[/tex]
[tex]D = 11.99[/tex] [tex]cm[/tex]
Therefore, the diameter of the circle is 11.99 cm
Answer:
Step-by-step explanation:
What does the statement I a I= 5 mean?
A a is equal to 5.
B a is equal to −5.
C a is 5 units from 0.
D You cannot tell without knowing the value of a.
If x = 10, what is the value of 5(x - 3)?
A. 7
B. 47
C. 35
D. 65
Look at the attached picture⤴
Hope it will help u..
Which of the following lines goes downwards from left to right?
O y= 2x + 5
O y=2x-6
O y= 2x
O y=-2x + 20
Answer:
D
Step-by-step explanation:
A line with a positive slope goes upwards from left to right.
A line with a negative slope goes downwards from left to right.
The given lines are all in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
y = 2x + 5 has m = 2 ← positive
y = 2x - 6 has m = 2 ← positive
y = 2x has m = 2 ← positive
y = - 2x + 20 has m = - 2 ← negative
Thus y = - 2x + 20 goes downwards from left to right
Answer:
D
Step-by-step explanation:
5. Find the area of a regular octagon with a radius of 12 ft. Round your answer to the nearest tenth, if
necessary
how do you write a quadratic equation in standard form?
Answer:
Powers of the variable descending left to rightright side of the equal sign is 0Step-by-step explanation:
For some constants a, b, and c, the standard form* is ...
ax^2 + bx + c = 0
___
It is nice if the leading coefficient (a) is positive, but that is not required.
The main ideas are that ...
Powers of the variable are descendingAll of the non-zero terms are on the left side of the equal signLike terms are combined_____
* This is the standard form for a quadratic. For other kinds of equations, when the expression is equal to zero, this would be called "general form."
Divide.
4.8 ÷ 10,000
Enter your answer as a decimal in the box.
The solution to 4.8 divided by 10,000 is 0.00048.
In Mathematics and Euclidean Geometry, an expression refers to a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we have the following mathematical expression;
4.8 ÷ 10,000
By rewriting in scientific notation form, we have:
[tex]4.8 \div 10^4[/tex]
By evaluating based on the exponent of 4, we have;
[tex]4.8 \times \frac{1}{10^4} \\\\4.8 \times 10^{-4}[/tex]
By rewriting as a decimal, we have:
0.00048.
The area of a trapezoid is 39 square millimeters. The height of the trapezoid is 8 millimeters. One of the base lengths of the trapezoid is 5 millimeters. What is the length of the other base of the trapezoid?
Answer: 18 meters
Step-by-step explanation:
I need feedback please. I don’t know how to solve this.
Answer:
79/9 * pi
Step-by-step explanation:
First find the circumference of the entire circle
C = 2 pi r
C = 2* pi* 5
C = 10 pi
The degree of MPN is 360 - 44 = 316
The fraction of the circle is 316/360 =79/90
Multiply that by the total circumference
79/90 * 10 pi
79/9 * pi
Answer:
s = 11π/9 units
Step-by-step explanation:
The arc length formula is s = rФ, where Ф is the central angle in radians.
Here the central angle is given as 44° and must be converted to radians:
44° π
------ * ----- = 11π/45 radians
1 180°
The length of arc MAN (not MPN) is s = (5 units)(11π/45 radians), or
s = 11π/9 units
The area of the polygon is 48 mi2. What is the length of side a? miles
To find the Length of Polygon Sides ('a') of a square polygon with an area of 48 mi², we apply the formula a = √Area. This gives a = √48 miles. This formula applies specifically to squares.
Given the area of the polygon is 48 square miles, to find the length of a side, we would first need to know the type of polygon.
For instance, if it's a square, the area is calculated by squaring one of its sides (Area = side²).
Here, to find the side length ('a'), we take the square root of the area. So, a = √Area.
Applying this to the given area, a = √48 miles.
However, please note that this formula is for a square.
Other polygons have different formulas for calculating such dimensions.
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What is the value of u? (Geometry problem)
Answer:
U = 71 degrees
Step-by-step explanation:
First you should set up an equation:
180 = b + (b - 19) + (180 - (b + 45))
Since there are 180 degrees in a triangle, set the sum of the angles equal to 180. And, since (u) and (b + 45) are supplementary angles that add up to 180, you can substitute (180 - (b + 45)) for (u).
Then, solve for (b):
180 = b + b - 19 + 180 - b - 45
180 = b + 116
64 = b
Find (b + 45):
64 + 45 = 109
Solve for (u):
180 - 109 = 71
u = 71
A cereal company is putting 1 of 3 prizes in each box of cereal. The prizes are evenly distributed so the
probability of winning any given prize is always 1/3
Mohamed wonders how many boxes he should expect to buy to get all 3 prizes. He carried out 24 trials of
a simulation and his results are shown below. Each dot represents how many boxes it took to get all 3
prizes in that trial.
3
4 5
6
7 8
9 10 11 12
# of boxes purchased
Use his results to estimate the probability that it takes more than 3 boxes to get all 3 prizes
Give your answer as either a fraction or a decimal
P(more than 3 boxes) C
Answer:
0.625
Explanation:
The image below was not posted for the but is needed to anser the question.
Further Explanation:
Mohamed carried out 24 trials of a simulation
Therefore, Total frequencies = 24
To get number of frequency greater than 3 we have to use the result in the result in the graph to obtain the estimate. Look at the graph below, when you count the dots that are on number of boxes purchased greater than 3, you will get 15.
Therefore, Number of frequency greater than 3 = 15
P(more than 3 boxes) = 15/24 = 0.625
Please help with this (Will mark brainliest if correct)
8.54
Simplest way to do it is using the Pythagorean Theorem
c^2 = a^2 + b^2
You want c. We can get a and b from the chart by seeing that the horizontal distance from A to B is 8 and the vertical distance is 3. Otherwise,
a = |-4| + 4 = 8, horizontal distance
b = |-5| + |-2| = 3, vertical distance
Then,
[tex]c = \sqrt{ {8}^{2} + {3}^{2} } = \sqrt{73} = 8.54[/tex]
Plz help! Kenneth's back yard is in the shape of a rectangle with a length of 12 yards and a width of 10 yards.A bag of grass seed costs $25.99 and covers 400 square feet.How much did Kenneth spend on grass seed to cover his back yard?
Answer:
EASY! First we have to find the area of the back yard.
Step-by-step explanation:
[tex]A=12*10\\A=120[/tex]
So, we have to convert feet to yards(as it's in feet and we are doing our calculations in yards).
(And also, due to the fact it's squared, we have to square our coefficient as well).
The formula states we have to divide by 3, thus:
[tex]\frac{400}{3^{2} } =\frac{400}{9 }=44.444...[/tex]
Hmmm. Might be better if we do it the other way around. Might be simpler.
Thus:
[tex]120*9=1,080[/tex]
So then we divide 1,080 by 400, as the bag covers 400 feet
[tex]\frac{1080}{400} =2.7[/tex]
So, he needs 3 bags(as he cannot use two to cover the entire back yard). He will have a little left over, but that's okay, because he cannot buy 0.7 of a bag.
Then we multiply this by the cost!
[tex]3*25.99=77.97[/tex]
So, Kenneth would have to pay $77.97 and have a little left over!
Hope I did this right!
Hope this helps!
P.S. How are you doing during this shelter-in-place?
When exchanging US Dollars (USD) for Philippine Peso (PHP) the number of Philippine Pesos
received is directly proportional to the number of US Dollars to be exchanged. If 350 USD can be
converted into 12,451.60 PHP.
Find the constant of proportionality k.
k=
(If needed, round answer to 3 decimal places.)
Using the k from above find the amount of PHP given that you have 700 USD to convert.
you will receive
PHP (If needed, round answer to 2 decimal places.)
Answer:
k = 35.57624,903.20 PHPStep-by-step explanation:
We want k such that ...
PHP = k·USD
Then the value of k is ...
PHP/USD = k = 12,451.60/350
k = 35.576
__
700 USD will convert to twice as much as 350 USD, so ...
700 USD = 700·35.576 PHP = 24,903.20 PHP
The constant of proportionality is 35.58. When you have 700 USD to convert, you will receive 24906.00 PHP.
Explanation:To find the constant of proportionality, we can use the formula:
k = y / x, where k is the constant of proportionality, y is the dependent variable (number of Philippine Pesos received), and x is the independent variable (number of US Dollars).
In this case, we have:
k = 12451.60 / 350 = 35.58 (rounded to 3 decimal places)
Now, to find the amount of PHP given 700 USD to convert, we can use the same formula:
PHP = k * USD
PHP = 35.58 * 700 = 24906.00 (rounded to 2 decimal places)
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The coffee shop where Juana works makes a profit of $312.50 for every 250 hot chocolates sold. How much
profit do they make on each hot chocolate sold?
The coffee shop makes a profit of on each hot chocolate sold. I know this because
Step-by-step explanation:
you have to first add and then divide with the percent you would need now try that
Answer:
1.25
Step-by-step explanati
312,50÷ 250
For all values of x, which expression is equivalent to 4(5x + 3) − 4x? A) 12x + 12 B) 16x + 12 C) 16x + 16 D) 32x + 12
Answer:
B) 16x + 12
Step-by-step explanation:
4(5x + 3) − 4x
= 20x + 12 - 4x
= 20x - 4x + 12
= 16x + 12
What is the slope of this question?
Answer: the slope is 1 up or down and one left or right (if you go down its a left if you go up its a right)
Step-by-step explanation:
Answer:
Step-by-step explanation:
hello :
this line passes trought A(0,1) and B(-1,0) the slope is :
(YB - YA)/(XB -XA)
= (0-1)/(-1-0) = -1/-1=1
other solution : the slope is tan x when x the angle betwen x-axis and this line ...tanx = 5/5=1
Which expression represents another method of computing the product given below?6.15*(-3.11)
Answer:
The expression that represents another method of computing
Is
615/100*(-311/100)
Step-by-step explanation:
Given the expression in decimal form, we can convert this to factional form and perform product operations as an alternative computational method
6.15*(-3.11)= 19.13
In fraction 6.15 can be written as
615/100
In fraction -3.11 can be written as
-311/100
Hence The product can also be expressed as fractions
615/100*(-311/100)
Answer:
(6 x (-3.11)) + (0.15 x (-3.11))
Step-by-step explanation:
In the given expression, the term 6.15 can be written as follows.
6.15 = 6 + 0.15
Apply the distributive property.
6.15 x (3.11) = (6 x (-3.11)) + (0.15 x (-3.11))
So, another method of computing the given product is given by the following expression.
6 x (-3.11)) + (0.15 x (-3.11))
Find the value of the expression.
X – (4 – y)
for x = 3 and y = 3
Answer:
2
Step-by-step explanation:
3-(4-3)=2
THIS IS URGENT HELPPPPP!!!!!!!!
What is the minimum value for g(x)=x^2−18x+79?
Answer:
(9,-2)
Step-by-step explanation:
hope i helped
An employee has a starting salary of $20,000 and can choose from two salary options:
Option 1: A salary increase by 5% each year.
Option 2: A guaranteed increase of $1,000 each year.
i. Which option is initially more beneficial?
ii. Which option is more beneficial after 10 years of employment?
iii. Explain your reasoning
Initially, both salary options provide the same increase, but after two years Option 1 becomes more beneficial due to compounding. After 10 years, the 5% annual increase of Option 1 provides a higher salary than the flat rate increase of Option 2.
Explanation:The salary options present themselves differently over time. Initially, Option 2, the guaranteed increase of $1,000 each year, is more beneficial. In the first year, a 5% increase on a $20,000 salary (Option 1) is only $1,000 - the same as Option 2. However, in the second year, the 5% increase is applied to the new salary of $21,000 (in Option 1), which gives an increase of $1,050 - thus, it surpasses Option 2.
After 10 years, Option 1 will be more beneficial. The reason lies in the principles of compounding; each year, the 5% increase is applied to the increased salary. Thus, in 10 years' time, the amount gained annually in Option 1 significantly surpasses the static $1,000 per year increase of Option 2.
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