Let's assume that "small", "medium" and "large" slushies sold are represented by "x", "y" and "z" respectively. The given information can be represented in the form of equations as:x + y + z = 250 ...(1)1.35x + 1.65y + 2.10z = 342.75 ...(2)Also, "They sold half as many mediums as the total of small and large combined" can be written as: y = (x + z) / 2 ...(3)Now, substituting equation (3) in (1) and (2), we get: x + (x + z) / 2 + z = 250 ...(4)2.70x + 3.75z = 585 ...(5)Multiplying equation (4) by 2, we get:2x + x + z + 2z = 500 ...(6)3x + 3z = 500 ...(7)Multiplying equation (3) by 2, we get:2y = x + z ...(8)Solving equations (7) and (8), we get: x = 60, y = 85, z = 105Therefore, 60 small, 85 medium and 105 large slushies were sold.
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According to the given information, the convenience store sold 48.73 small size slushies, 62 medium size slushies, and 76.27 large size slushies.
A convenience store has three different sizes of slushies.
The small sells for 1.35, the medium sells for 1.65 and the large sells for 2.10.
They sold 250 slushies in one day and made 342.75.
They sold half as many mediums as the total of small and large combined.
Let x be the number of small size slushies sold
Then, y be the number of medium size slushies sold and z be the number of large size slushies sold
The equations to be used are:
x + y + z = 250 [as they sold 250 slushies in one day]
1.35x + 1.65y + 2.10z = 342.75 [as they made 342.75]
y = (x + z)/2 [as they sold half as many mediums as the total of small and large combined]
Substitute the value of y in first two equations
1. x + y + z = 250
⇒ x + (x + z)/2 + z = 250
⇒ 2x + z = 250 - z .....(1)
2. 1.35x + 1.65y + 2.10z = 342.75
⇒ 1.35x + 1.65((x + z)/2) + 2.10z = 342.75
⇒ 2.70x + 1.65z = 342.75 - 1.65z .....(2)
Multiply equation (1) by 1.65 and subtract it from equation (2)
2.70x + 1.65z - [1.65(2x + z)] = 342.75 - 1.65z - [1.65(250 - z)]
⇒ 2.70x + 1.65z - 3.30x - 1.65z = 342.75 - 412.50/1.65
⇒ -0.60x = -29.24
⇒ x = 48.73
Then substitute this value in equation (1)
2x + z = 250 - z
⇒ 2(48.73) + z = 250 - z
⇒ 2z = 250 - 2(48.73)
⇒ 2z = 152.54
⇒ z = 76.27
Finally, substitute the value of x and z in y = (x + z)/2y = (48.73 + 76.27)/2
⇒ y = 62
The convenience store sold: 48.73 small size slushies, 62 medium size slushies, and 76.27 large size slushies.
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Two similar-looking series are given. Test each one for convergence or divergence.
∑_(n=1)^[infinity]▒〖( n/n^2 +3)〗
O convergent
O divergent
∑_(n=1)^[infinity]▒( n/n^2 +3) ^n
O convergent
O divergent
1. Series:
[tex]\[\sum_{n=1}^{\infty} \frac{n}{{n^2 + 3}}\][/tex]
To determine the convergence or divergence of this series, we can use the comparison test or the limit comparison test.
Using the comparison test:
We compare the given series with a known series that we know to be convergent or divergent. Let's consider the series [tex]\(\sum_{n=1}^{\infty} \frac{1}{n}\).[/tex]
As [tex]\(n\)[/tex] approaches infinity, the term [tex]\(\frac{n}{{n^2 + 3}}\)[/tex] is always less than or equal to [tex]\(\frac{1}{n}\).[/tex]
Since the series [tex]\(\sum_{n=1}^{\infty} \frac{1}{n}\)[/tex] is a known divergent harmonic series, and the terms of our series are less than or equal to the corresponding terms of the harmonic series, we can conclude that our series is also divergent.
Therefore, the first series is divergent.
2. Series:
[tex]\[\sum_{n=1}^{\infty} \left(\frac{n}{{n^2 + 3}}\right)^n\][/tex]
To test the convergence or divergence of this series, we can use the root test or the ratio test.
Using the root test:
We take the [tex]\(n\)th[/tex] root of the absolute value of the series term and check the limit as [tex]\(n\)[/tex] approaches infinity.
Let's calculate the limit:
[tex]\[\lim_{{n\to\infty}} \left(\frac{n}{{n^2 + 3}}\right)^n = \lim_{{n\to\infty}} \left(\frac{n^n}{{(n^2 + 3)^n}}\right) = \lim_{{n\to\infty}} \left(\frac{n^n}{{n^{2n} + 3n}}\right) = \lim_{{n\to\infty}} \left(\frac{n^n}{{n^{2n}}}\right) = \lim_{{n\to\infty}} \left(\frac{1}{{n^n}}\right) = 0\][/tex]
Since the limit is less than 1, the root test tells us that the series converges.
Therefore, the second series is convergent.
In summary:
1. The first series is divergent.
2. The second series is convergent.
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Quick wats 5+5?????
Not even my granny knows!!!!!
(for those confused it`s a joke)
Answer:
Hehe, I get it mate
Step-by-step explanation:
5 + 5 = 10
Which of the following describes the dimensions of a backyard?
The area of the yard.
The perimeter of the yard.
The volume of the yard.
The lengths of the sides of the yard.
Answer:
the lengths of the sides of the yard.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
this reason is because the sides tell how big your backyard is
PLEASE HELP THIS IS TIMED!!!
Answer:
its c. 1/4
hope it helps;)
Answer:
1/4
Step-by-step explanation:
1. Look at the numbers on the number line (1,0,-1)
2. See where the point falls in between. (0 & 1)
3. Since the point is closer to 0 you can infer that it is 1/4
I need this pls help me
Answer:
that statement is true
is there some other question?
Answer:
it is true
Step-by-step explanation:
given: pfst is a rectangle, m∠sot=60°, os = r=4 find: st and pt
The dimensions of the provided rectangle's sides ST and PT are 4 and 4√3 units, respectively.
Given: PFST is a rectangle with a radius of four and angle SOT of 60 degrees.
We must locate ST and PT.
We will thus apply the idea of cosine of an angle to find the same.
The law of cosine is expressed as follows for a triangle with sides α, β, and γ with angles, and:
[tex]\mathrm {b^2=a^2+c^2-2ac\cdot \cos \left(\beta \right)}[/tex]
Since the radius of the circle O is made up of the points OS, OP, OF, and OT, their measurements are all equal.
Now, considering the Δ SOT for ST.
We have,
β = 60° and a and c = 4.
Applying the law:
[tex]\mathrm b=\sqrt{4^2+4^2-2\cdot \:4\cdot \:4\cos \left(60^{\circ \:}\right)}[/tex]
Solving we get,
b = 4
Therefore, ST = 4 units.
Similarly, considering the Δ POT for PT.
Here, ∠POT = 180° - 60° [linear pair]
∠POT = 120°
So, we have,
β = 120° and a and c = 4.
Applying the law:
[tex]\mathrm b=\sqrt{4^2+4^2-2\cdot \:4\cdot \:4\cos \left(120^{\circ \:}\right)}[/tex]
Solving we get,
b = 4√3 units
Therefore, PT = 4√3 units.
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The figure is given below:
DEPRECIATION The value of a new tractor decreases by 20% each year. The initial cost of a tractor is $38,000. Write a function f(t) that can be used to project the value of the tractor t years in the future.
Answer:
y = 0.20x(-38,000) + 38,000
Step-by-step explanation:
y: represents how much the price is now.
x: Represents the number of years passed.
y = 0.20x(-38,000) + 38,000
For example if it's 1 year
y = 0.20(1) (-38,000) + 38,000
y = 0.20(-38,000) + 38,000
y = -7600 + 38,000
y = 30,400
What is (6x2 - 11x + 4) = (2x - 1)?
A. 2x - 1
B. 3x - 4
C. -8x + 4
D. 3x - 7
Answer:
A
Step-by-step explanation:
got it right on edg
which would best display the following data if you wanted to display the numbers which are outliers as well as the mean
A stem and leaf plot would best display the following data if you wanted to display the numbers which are outliers as well as the mean. Option C is the correct option.
A stem and leaf plot would be the best choice for displaying the given data if the goal is to show outliers as well as the mean. A stem and leaf plot is a simple and effective way to represent the data distribution while preserving the individual data points.
It organizes the data by separating the leading digit (stem) and the trailing digit (leaf). This plot allows for easy identification of outliers as they would be displayed separately from the main distribution. Additionally, the stem and leaf plot can include a line indicating the mean, providing a visual representation of its position relative to the data points.
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The question is -
Which would best display the following data if you wanted to display the numbers which are outliers as well as the mean?
[4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32]
A. Pie chart.
B. Bar graph.
C. Stem and leaf plot.
D. Venn diagram.
a polynomial function h(x) has a zero of x = 3 – 4i with a multiplicity of one. certain values of h(x) are given in the following table.
The polynomial function h(x) has a complex zero at x = 3 – 4i with a multiplicity of one. The given table provides certain values of h(x) for various x-values.
A zero of a polynomial function corresponds to the values of x for which the function evaluates to zero. In this case, the zero is x = 3 – 4i, where 4i represents the imaginary unit multiplied by 4. The multiplicity of one indicates that this zero occurs only once in the function.
The table provides specific values of h(x) for different x-values, which allows us to observe the behavior of the function. However, without knowing the functional form of h(x) or additional information, we cannot determine the complete polynomial equation.
To fully determine the polynomial function h(x) based on the given zero, we need to know all of its zeros, including any real or complex zeros with their respective multiplicities. Additionally, the degree of the polynomial can affect the number of zeros it possesses. With this information, we could reconstruct the polynomial equation using methods such as factoring, synthetic division, or the quadratic formula.
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A polynomial function h(x) has a zero of x = 3 – 4i with a multiplicity of one. Certain values of h(x) are given in the following table.
x h(x)
–5 0
–2 3
–1 0
1 2
4 0
7 6
10 0
If every real x-intercept of h(x) is shown in the table and each has a multiplicity of one, what is the degree of h(x)?
3
4
5
6
The stemplet below displays midterm exam scores for 34 students taking a calculus course. The highest possible test score was 100. The teacher declared that an exam grade of 65 or higher was good enough for a grade of C 4148 53344 62335567 10012356 81135 9039 The percent of students who did not cam a grade of C or higher (as declared by the teacher) is closest to a 65% 26.35% 50% 80% QUESTION 3 A group of veterinary researchers plans a study to estimate the average number of enteroliths in horses suffering from them. Previous research has shown the variability in the number to be -2. The researchers with the margin of error to be no larger than 0.5 for a 99% confidence interval. To obtain such a margin of error, the researchers nood at least: Ca 107 observations b.54 observations c5) observations. 106 observations
Based on the given information, the correct answer is: c) 105 observations
To calculate the required sample size, we can use the formula:
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-score corresponding to the desired level of confidence (for a 99% confidence level, Z = 2.576)
σ = standard deviation or variability
E = desired margin of error
Given:
Variability (standard deviation) = 2
Margin of error (E) = 0.5
Z = 2.576 (corresponding to a 99% confidence level)
Plugging in the values into the formula:
n = (2.576 * 2 / 0.5)^2
n = 10.304^2
n ≈ 106.01
Rounding up to the nearest whole number, the researchers would need at least 106 observations to obtain a margin of error no larger than 0.5 for a 99% confidence interval. Therefore, the correct answer is c) 105 observations.
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The radius of a sphere is 6 units.
Which expression represents the volume of the sphere,
in cubic units?
6
07(6)
0 -1(6):
07(12)
07(12)
Save and Exit
Next
Submit
Answer:
choice 2) 4/3πr³
Step-by-step explanation:
The volume of the sphere is 678.24 u³
V = ⁴⁄₃ * π * (6u)³
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
To calculate the volume of a sphere we have to use the following formula:
V = volume
r = radius = 6 units
π = 3.14
V = ⁴⁄₃πr³
we replace with the known values
V = ⁴⁄₃ * 3.14 * (6u)³
V = 4.187 * 216 u³
V = 678.24 u³
The volume of the sphere is 678.24 u³
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An office is ordering pizza for two groups. of the 25 workers in accounting, 72% want pepperoni. Pls help
Answer:
18/25
Step-by-step explanation:
please help I give brainliest
I don't want to see an link
If I do you will reported
Answer will give brainliest!
Answer:
One point would be on (0,0) and the other on (1,-5)
Step-by-step explanation:
hope this helped :)
Find the value of each variable. If your answer is not an integer, write it in simplest radical form with the denominator rationalized
Answer:
I would need to see the variables to answer this questions.
15. A ball is dropped from a 75 foot tall tower, and the height of the ball (in feet) can be represented by the
equation h = -16t? + 75 where t is time (in seconds). Determine the amount of time it will take for the ball
to hit the ground. Round your answer to the nearest hundredth of a second.
Find the linear polynomial p(x) = djx + do, = that interpolates the two points with coordinates (3,0) and (4, -3). The coefficients of p(x) are aj = ao =
In order to interpolate between the two points (3,0) and (4,-3), the linear polynomial p(x) is equal to -3x + 3, and this equation is employed. The value of the constant term is 3, but the value of the coefficient x is -3.
A linear polynomial is a type of polynomial that has only one degree of complexity. This suggests that it can be stated using the formula p(x) = axe + b, where a and b are values that continue to be the same. a and b are values that remain unchanged. These two sentences inform us that the value of p(3) is zero, and that the value of p(4) is negative three. When we enter these values into the equation p(x) = axe + b, we obtain the two equations that are presented further down in this section:
0 = 3a + b -3 = 4a + b
Following the resolution of the equations for a and b, we find that the respective solutions are a = -3 and b = 3. Since this is the case, the linear polynomial p(x) that interpolates the two points (3,0) and (4,-3) is -3x + 3, as was demonstrated in the preceding sentence.
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a race car has wheels with diameter 66 cm. if a formula 1 car is in a 300 km race, how many times must the tires turn to cover the race distance?
A race car with wheels with diameter 66 cm must turn 1,088,000 times to cover a 300 km race. This is because the circumference of a wheel is equal to its diameter multiplied by pi, which is approximately 3.14.
So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.
The circumference of a circle is equal to its diameter multiplied by pi, which is approximately 3.14. So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.
In other words, the car must turn its wheels 1,445 times to cover the race distance. This is a lot of turns, but it is possible for a Formula 1 car to do this. The cars are designed to be very efficient and to have very low rolling resistance, which means that they can turn their wheels very quickly without losing too much energy.
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An advertisement for a new toothpaste states that 64% of users reported better dental checkups. The results of the poll are accurate within 3.4 percent points, 9 times out of 10. (A) State the confidence level. (B) Determine the confidence interval. (C) If all 32 students in a mathematics class used this toothpaste, determine the range of the mean number of classmates who could expect better dental checkups.
(A) The confidence level for the results of the poll is 90%
(B) The confidence interval is (58.411, 69.589).
(C) The range of the mean number of classmates who could expect better dental checkups is approximately 1867 to 2229.
(A) The confidence level for the results of the poll is 90%. This means that there is a 90% probability that the true percentage of users reporting better dental checkups falls within the stated range.
(B) To determine the confidence interval, we need to consider the margin of error. The margin of error is calculated by multiplying the critical value (obtained from a standard normal distribution table) by the standard deviation of the sample proportion. In this case, the standard deviation is determined by the given accuracy of 3.4 percent points.
Using a critical value of 1.645 (corresponding to a 90% confidence level), we can calculate the margin of error as 1.645 times 3.4, which equals 5.589.
To find the confidence interval, we subtract and add the margin of error from the reported percentage of users who reported better dental checkups. Subtracting 5.589 from 64 gives us a lower bound of 58.411, and adding 5.589 gives us an upper bound of 69.589. Therefore, the confidence interval is (58.411, 69.589).
(C) If all 32 students in a mathematics class used this toothpaste, the range of the mean number of classmates who could expect better dental checkups can be calculated by applying the confidence interval to the sample size. Taking the lower bound of the confidence interval (58.411) and multiplying it by 32, we get 1867.552. Rounding down, we have a minimum estimate of 1867 classmates who could expect better dental checkups.
Similarly, multiplying the upper bound of the confidence interval (69.589) by 32 gives us 2228.448. Rounding up, we have a maximum estimate of 2229 classmates who could expect better dental checkups.
Therefore, the range of the mean number of classmates who could expect better dental checkups is approximately 1867 to 2229.
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Please help me on this question if you would want brianleist!! Tank yah!! ^^
Answer:
Origin
Step-by-step explanation:
Origin is the starting points (0,0)
Hope this helped :)
HELP DUE IN 10 MINUTES
I put 16 and it said that it was Wong
Answer: 97/100
Step-by-step explanation:
Answer:
The answer is 0.97 or 97/100
Step-by-step explanation:
9/10 = 0.9
7/100 = 0.07
0.9 + 0.07 = 0.97
Hope this helps!
Please mark as brainliest!
3(2 - b) < 10 - 3(b-6)
After simplifying the inequality we get 6 < 28 which is true. Hence the given statement is true.
An inequality is a mathematical statement that uses the inequality symbol to indicate the relationship between two expressions. Both sides of an inequality sign have different expressions.
It signifies that the expression on the left should be more or smaller than the expression on the right, or vice versa. Literal inequalities occur when the relationship between two algebraic expressions is defined using inequality symbols.
The given inequality is:
3(2 - b) < 10 - 3(b-6)
Distribute the number inside the bracket,
6 - 3b < 10 - 3b + 18
Add 3n on both sides,
6 < 10 + 18
Simplifying it,
6<28
Hence,
The given statement is true.
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The complete question is:
Check whether the statement is true or false:
3(2 - b) < 10 - 3(b-6)
find the slope. 0,3 and 2,0
Answer:
Step-by-step explanation
y2-y1 over x2-x1
0-3 = -3
2-0 = 2
So answer is:
-3/2
Answer: The slope is -3/2 or 1 1/2 simplified
Hope it helped :D
Please mark me brainliest
Solve the following: four and six tenths plus six and eight tenths
Answer:
4 6/10+ 6 8/10= 11 4/10
Step-by-step explanation:
The 4+6=10, and 6/10+8/10=14/10 which converts to 1 4/10. 10+1 4/10= 11 4/10
Answer:
11 and 4/10
Step-by-step explanation:
Hope this helps!
Calculate the flux of the vector field (³, ³), out of the annular region between the x² + y² = 9 and x² + y² = 16.
Given that the vector field F is (3x, 3y) and the region is an annular region between the circles x² + y² = 9 and x² + y² = 16,To calculate the flux of the vector field, we use the formula: flux = ∬F · dS, Where F is the vector field and dS is an elemental vector area.
Using cylindrical coordinates: For the outer circle x² + y² = 16, the limits of θ are from 0 to 2π and the limits of r are from 4 to 4√2. For the inner circle x² + y² = 9, the limits of θ are from 0 to 2π and the limits of r are from 3 to 3√2.The vector normal to the surface at a point (r,θ) is given by n = (cosθ, sinθ, 0).
Hence, the outward normal vector is given by n = (cosθ, sinθ, 0) and the elemental vector area is given by dS = r dr dθ.Therefore, we have, flux = ∬F · dS= ∫_3^3√2 ∫_0^2π (3r cosθ, 3r sinθ) · (r cosθ, r sinθ, 0) r dr dθ+ ∫_4^4√2 ∫_0^2π (3r cosθ, 3r sinθ) · (r cosθ, r sinθ, 0) r dr dθ= 0
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A spinner is divided into 8 equal sections: 4 red, 2 white, 1 green, and 1 blue. What is the probability that the spinner lands on blue or white?
Answer:
3/8
Step-by-step explanation:
Total = 8
Probability of blue: 1/8
Probabiity of white: 2/8
Probbility of blue AND white:
1/8 + 2/8
3/8
Answer:
3/8
Step-by-step explanation:
because there are 3 possbile places the spinner can go, and that there are 8 sections, the answer is 3/8
The volume of a cylinder is 256pi in 3 and the height of the cylinder is 1 in what is the radius of the cylinder
Answer:
I got 9.03
Step-by-step explanation:
the formula is V=pir2h
(pi, radius squared, and height)
anyone know this answer??
Answer:
two
Step-by-step explanation:
The exact value of sec(60°) sec ( 60 ° ) is 2 .