The amounts needed to make 6 servings are given as follows:
Sauce: 12 servings.
Oregano: 3/4 teaspoons.
Here, we have,
The needed amounts to make 6 servings of the recipe are obtained applying the proportions in the context of the problem.
From the first line of the table, we get the amounts of sauce and oregano per serving are follows:
Sauce: 8/4 = 2 cups.
Oregano: 0.5/4 = 1/8 teaspoons per serving.
Hence the amounts for six servings are given as follows:
Sauce: 6 x 2 = 12 servings.
Oregano: 6 x 1/8 = 6/8 = 3/4 teaspoons.
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Find the value of a
Answer is 3
Step-by-step explanation:
Use the Ratio Test since Ratio Test guarantee absolutely convergence.
[tex] \frac{ ( - 1) {}^{k + 1}(k + 1) {}^{a} }{5 {}^{k + 1}(3(k + 1) } \times \frac{5 {}^{k}(3k) }{(k) {}^{a} ( - 1) {}^{k} } [/tex]
This simplifes to
[tex] \frac{( - 1) {}^{k} ( - 1) ((k + 1)!) {}^{a} }{5 {}^{k}(5)(3k +1) ! } \times \frac{5 {}^{k} (3k)!}{( - 1) {}^{k} (k!) {}^{a} } [/tex]
[tex] \frac{ - (k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]
Take the absolute value
[tex] \frac{(k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]
In order for this series to be convergent,
the limit as k approaches infinity must be less than 1.
In order for this series to have a limit less than 1, our numerator and denominator degree must be equal or the denominator must have the larger degree.
Why
If the numerator has a larger degree, our test would make this divergent, so the limit would be infinity
Since the denominator have 3 binomials, our power for the denominator will be 3, this the numerator having a degree of 3 or less as well.
So one of the answer is 3.
Number 1 please help
Answer:
x^2y^4
Step-by-step explanation:
b because u have to add the exponents of the like variable. x^4 and x^-2 are the like terms in this equations so 4+(-2) so its basically flipping the signs plus and the negative sign so it's just -2
Which expression is equivalent to 12/5x -2 A. 12x-2/5 B. 2(2/5x -1) C. 2/5(6x-10) D. 1/5(12x-10)
Answer:
The answer is D.
[tex] \frac{1}{5}(12x - 10)[/tex]
The half-life of a certain element is 5 days. If you started with 948 grams of this element, how much remains after 30 days?
After 1 half-life, the amount of the element remaining is half of the original amount. After 2 half-lives, the amount remaining is half of the remaining amount after the first half-life. We can continue this pattern until we get to 30 days.
The number of half-lives in 30 days is 30/5 = 6.
So, after 1 half-life, the amount remaining is 948/2 = 474 grams.
After 2 half-lives, the amount remaining is 474/2 = 237 grams.
After 3 half-lives, the amount remaining is 237/2 = 118.5 grams.
After 4 half-lives, the amount remaining is 118.5/2 = 59.25 grams.
After 5 half-lives, the amount remaining is 59.25/2 = 29.625 grams.
After 6 half-lives, the amount remaining is 29.625/2 = 14.8125 grams.
Therefore, after 30 days, 14.8125 grams of the element remains
NEED TO BE DONE ASAP ONLY HAVE 2MIN
Answer:
42 units³
Step-by-step explanation:
You want the volume of a rectangular prism that has a base area of 5 1/4 units² and a height of 8 units.
VolumeThe formula for the volume of a prism is ...
V = Bh
where B is the base area and h is the height perpendicular to the base.
Here, we have B = 5 1/4 u² and h = 8 u. The volume is ...
V = (5 1/4 u²)(8 u) = 42 u³
The volume of the prism is 42 cubic units.
Factor each polynomial using difference of squares. Check for common factors first.
a) x² – 36
b) 3x² - 12
Factor the following using the trinomial method. Check for common factor first.
a) x² + 6x + 9
b) 4x² - 8x - 60
PLS HELP!!!!! I ONLY HAVE 2 HOURS!!!
The results of factoring the polynomials are (x - 6)(x + 6), 3(x - 2)(x + 2), (x + 3)² and 4(x + 3)(x - 5)
Factoring using difference of squaresFirst, we have
x² – 36
Applying the property of difference of squares, we have
(x - 6)(x + 6)
Next, we have
3x² - 12
Factor out 3
3(x² - 4)
Applying the property of difference of squares, we have
3(x - 2)(x + 2)
Factoring the following using the trinomial methodFirst, we have
x² + 6x + 9
Expand and factorize
x² + 6x + 9 = x² + 3x + 3x + 9 = (x + 3)²
Next, we have
4x² - 8x - 60
Expand and factorize
4x² - 8x - 60 = 4(x² - 2x - 15) = 4(x + 3)(x - 5)
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find f(g(2)), g(f(2)) given f(x)=3x+5 and g(x)=-7x+6
The two compositions give:
f(g(2)) = -19g(f(2)) = -71How to evaluate the compositions?Here we have two functions:
f(x) = 3x + 5
g(x) = -7x + 6
And we want to fin the two compositions:
f(g(2))
g(f(2))
First, let's find g(2) = -7*2+ 6 = -14 + 8 = -8
Then:
f(g(2)) = f(-8) = 3*-8 + 5 = -19
Now the other one:
f(2) = 3*2 + 5 = 11
Evaluating g in that:
g(11) = -7*11 + 6 = -77 + 6 = -71
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When signing the lease for his $750.00 per month rental property. Stanley will have to pay the first and last months rent and a security deposit equal to 30% of one month's rent. If Stanley currently earns an average bi-weekly net pay of $1,050.00, determine what percent of his monthly pay he will need to save if he wants to save enough money to sign the lease in three month.
Answer:
Step-by-step explanation:
tax
A car is driving away from El Paso with constant velocity. At 1 p.m., it is 145 miles away from El Paso. At 3 p.m., it is 275 miles away from El Paso.
Part A: Write a linear function that describes the distance (in miles) the car is from El Paso in terms of time (in hours after 12:00 p.m.).
The linear function that describes the distance (in miles) is therefore y = 65x + 80
How to solve for the linear functionWe have to find the slope and the intercept in other to get the linear function
The data points are:
(1, 145) and (3, 275).
m = (y2 - y1) / (x2 - x1)
fixing the data points we have
m = (275 - 145) / (3 - 1)
= 130 / 2
= 65
y = mx + b
(1, 145):
145 = 65(1) + b
b = 145 - 65
= 80
y intercept is 80
The linear function is therefore y = 65x + 80
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Complete the ratio table
The missing values from ratio table are 17 and 28.
We have table as
3 1
48 16
51 x
78 26
84 y
So, the ratio are in proportion then
48 / 16 = 51 /x
3 = 51/x
x= 51/3
x = 17
and, 3/1 = 84/y
y= 84/3
y= 28
Thus, the values are 17 and 28.
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A hair dryer has a power of 1,200 W. How much electrical energy does it use in minutes?
Answer:
r 0.6 kWh to run for 30 minutes.
Answer:
ok so it takes 1200 watts for a hair dryer to run for a full hour, that means it takes 600 watts, or 600 Wh, or 0.6 kWh to run for 30 minutes
Step-by-step explanation:
Find a linear inequality with the following solution set. Each grid line represents one unit.
[asy]
size(200);
fill((2,-5)--(-5,-5)--(-5,5)--(5,5)--(5,-2)--cycle,yellow);
real ticklen=3;
real tickspace=2;
real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label("$\textnormal{Re}$",(xright,0),SE);
label("$\textnormal{Im}$",(0,ytop),NW);
} else {
label("$x$",(xright+0.4,-0.5));
label("$y$",(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i 0.1) {
TicksArrx.push(i);
}
}
for(i=ybottom+ystep; i 0.1) {
TicksArry.push(i);
}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.1),extend=true),p=invisible);//,above=true);
yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.1),extend=true), p=invisible);//,Arrows);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=black, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=black, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
draw((5,-2)--(2,-5),dashed+red, Arrows(size=axisarrowsize));
rr_cartesian_axes(-5,5,-5,5);
for( int i = -4; i <= 4; ++i) {
draw((i,-5)--(i,5));
draw((-5,i)--(5,i));
}
[/asy]
(Give your answer in "standard form" $ax+by+c>0$ or $ax+by+c\geq0$ where $a,$ $b,$ and $c$ are integers with no common factor greater that 1)
I’ve looked at other people’s answers but my website keeps saying im wrong. If anyone knows how to register this answer to aops, please tell me how
The linear inequality with the solution set (2,-5), (-5,-5), (-5,5), (5,5), (5,-2) are x ≤ 5 and y ≤ 5
Finding a linear inequality with the solution setThe solution set is given as
(2,-5), (-5,-5), (-5,5), (5,5), (5,-2)
We can see that the highest y value in the above ordered pairs is 5
So, we have
y ≤ 5
Also, we can see that the highest x value in the above ordered pairs is 5
So, we have
x ≤ 5
Hence, the linear inequality with the solution set is x ≤ 5 or y ≤ 5
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What is the measure of angle b?
Answer:60 degrees
Step-by-step explanation: The three angles of a triangle add to 180, a right angle is 90 so 180-90-30= 60.
A rectangular aquarium measures 21 inches long by 11 inches wide by 18 inches tall. If the aquarium is filled to the 15 inch mark, what is the volume of the water in the aquarium?
The volume of water in the aquarium up to the 15 inch mark is 3465 cubic inches.
What is the volume of the water in the aquarium?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length
The volume of water in the aquarium up to the 15 inch mark will be equal to the volume of a rectangular prism with a length of 21 inches, a width of 11 inches, and a height of 15 inches.
This is because the water level is 15 inches from the bottom of the aquarium.
Hence, the volume of water in the aquarium up to the 15 inch mark is:
V = l × w × h
V = 21 × 11 × 15
V = 3465 cubic inches
Therefore, the volume of water in the aquarium is 3465 cubic inches.
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Evaluate the expression
12-3y divided by 2 + y(2y-4 divided by y) for y = 3
Donovahn made two bracelets for a friend. Each bracelet is made of 36 beads. Bracelet A contains 12 letter beads Bracelet B contains 20 letter beads. Which statement is true?
Based on the conditions, the correct statements are,
⇒ Bracelet B has 8 more letter beads than Bracelet A.
We have to given that;
Donovahn made two bracelets for a friend.
And, Each bracelet is made of 36 beads. Bracelet A contains 12 letter beads Bracelet B contains 20 letter beads.
Hence, We have;
Based on the information provided, we can say that Bracelet B contains more letter beads than Bracelet A.
Specifically, Bracelet B has 8 more letter beads than Bracelet A.
Thus, Based on the conditions, the correct statements are,
⇒ Bracelet B has 8 more letter beads than Bracelet A.
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The Statue of Liberty in New York Harbor stands at a height of about 305 feet. A group of students in a social studies class is building a scale model of the monument. If the students use a scale of 1 inch: 50 feet, about how tall will their model be? Round your answer to the nearest tenth of an inch if necessary.
Answer:
The answer to your problem is, 6.1 inches
Step-by-step explanation:
So we know that 1 inch of there model in real life is 50 feet.
Divide:
305 / 50
= 6.1 but we are going to use 6
Since it is 6 there model is 6 inches.
But remember we still have that 0.1 which we need to full fill for that:
Note that 6.1 will be in inches.
So it is done.
Thus the answer to your problem is, 6.1 inches
UCM college administrators claim that the average freshman enrollment over the last 10 years meets the university's capacity of 6,500 students. You believe hypothesize this is inaccurate and believe that UCM is underestimating the number of college freshman. Using a sample of 500
students, you determine a sample mean of 6,600 freshman. Assume o = 1,000 and a = .05.
The t-statistic value of the hypothesis is 2.236
The population mean is equal to 6,500 (H0: μ = 6500)
Alternative hypothesis:
The population mean is greater than 6,500 (Ha: μ > 6500)
We are given the sample mean (x) = 6,600, sample size (n) = 500, population standard deviation (σ) = 1,000, and level of significance (α) = 0.05.
First, we need to calculate the t-statistic using the formula:
t = (X - μ) / (σ / √n)
where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values, we get:
t = (6,600 - 6,500) / (1,000 / √500)
= 2.236
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
What type of correlation is suggested by the scatter plot?
Positive, weak correlation
Negative, weak correlation
Positive, strong correlation
Negative, strong correlation
No correlation
A baker produces 400 brownies a day at a cost of 25 cents per brownie. If all the brownies are sold each day, what is the minimum selling price per brownie to make a daily profit of at least $420?
The minimum selling price per brownie to make a daily profit of at least $420 is $1.30.
What is the minimum selling price per brownie to make a daily profit of at least $420?Given that: A baker produces 400 brownies a day at a cost of 25 cents per brownie.
Let's begin by calculating the total cost of producing 400 brownies a day:
Cost per brownie = 25 cents = 0.25 dollars
Total cost = 400 × 0.25 = 100 dollars
To make a daily profit of at least $420, the total revenue should be:
Total revenue = Total cost + Minimum profit
Total revenue = 100 + 420 = 520 dollars
The minimum selling price per brownie to achieve this revenue can be calculated as:
Selling price per brownie = Total revenue / Number of brownies produced
Selling price per brownie = 520 / 400
Selling price per brownie = 1.3 dollars
Therefore, the minimum selling price is $1.30 per brownies.
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Pamela paid $8.95 for 5 pounds of bananas. How much will it cost to buy 2 pounds of bananas at the same rate?
Answer:
$3.58
Step-by-step explanation:
Because we know that the 2 lbs of bananas will be purchased at the same rate, the price per pound for 5 lbs of bananas is proportional to the price per pound for 2 lbs of bananas.
Thus, we can solve for price, p of 2 lbs of bananas by setting up a proportion:
[tex]\frac{8.95}{5}=\frac{p}{2}\\ \\ 17.90=5p\\\\3.58=p[/tex]
determine he measures of the angles
Answer:
45
Step-by-step explanation:
A mixture of 50% alcohol and 50% water has 4 liters of water added to it. It is now 25% alcohol. What was the total volume of the original mixture? (Please mention the numeric value.)
The total volume of the original mixture is 4 liters.
Given that:
A mixture of 50% alcohol and 50% water has 4 liters of water added to it. It is now 25% alcohol.
Let 'x' be the amount of water and alcohol. Then we have
x / (x + x + 4) = 0.25
x/(x + 2) = 0.5
2x = x + 2
x = 2
The total volume of the original mixture is calculated as,
Total volume = x + x
Total volume = 2 + 2
Total volume = 4 liters
The total volume of the original mixture is 4 liters.
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The ratio of two numbers is 1 to 3 and the sum of their squares is 250. Find the numbers.
Answer:
Step-by-step explanation:
5 and 15
5^2=25
15^2=225
225+25=250
DE bisects AC at point B. AC=a+23
and AB = 3a + 4. Find BC.
Y
X
13
2
X
(X) XS
X₁
IV
The values of AB and BC are equal and equal to
13 units.How to find BCInformation given in the problem includes
DE bisects AC at point B
AC = a + 23
AB = 3a + 4
From the definition of a bisector, point B divides AC into two equal sides, this means that
AB = BC = (1/2) * AC
Substituting the value of AC and AB
AB = 3a + 4 = (1/2) * (a + 23)
3a + 4 = (1/2) * (a + 23)
solving for a
2 * (3a + 4) = a + 23
6a + 8 = a + 23
6a - a = 23 - 8
5a = 15
a = 3
Then we have that:
AB = 3a + 4 = 3(3) + 4 = 9 + 4 = 13
and, AB = BC
so BC = 13
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If this figure is cut along the dotted line, what 2 shapes will be made?
The shapes that would be made if the figure is cut along the dotted line are a right angled- triangle and a semi - circle.
How to find the shapes ?Upon reviewing this shape, we observe that it is comprised of two distinct shapes: a right-angled triangle and a semicircle.
This means that if the figure was cut along the dotted lines that joined them, the shapes that would be made are the same shapes which are a right triangle and a semi - circle.
In conclusion, the shapes would be a semi - circle and right triangle.
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In circle E, EF = 10 and m
ZFEG = 72°. Find the length of FG.
Express your answer as a fraction times π.
Answer:
Length of FG=
The length of the arc FG is 12.56 units
What is length of an arc?Length of an arc is the distance that runs through the curved line of the circle making up the arc.
An arc is a cut out section of a circle. The circumference is the whole body of the circle.
The length of an arc is expressed as
(tetha))360 × 2πr
where r is the radius and tetha is the angle between the radii.
l = 72/360 × 2 × 3.14 × 10
l = 4521.6/360
l = 12.56 units
therefore the length of the arc FG is 12.56 units
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In the diagram, angle adc is a central angle and angle measure adc = 60°. What is angle measure ABC?
The measure of angle ABC is 30 degrees. Option B
How to determine the valueIt is important to note the properties of a circle, they include;
Two circles are congruent if they have same radii.Diameter of a circle is the longest chord in the given circleSame chords of a circle subtend the same measure of angles at the center of the circleThe radius that is perpendicular to the chord divides the chord into twoAlso note that the measure of the angle at the circumference is half to twice the measure of the angle at the center.
From the information given, we have that;
<ADC = 60 degrees
This is the angle at the circle
Then,
<ABC is the angle at the circumference
<ABC = <ADC/2 = 60/2 = 30 degrees
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Select the correct answer. Which graph represents the given exponential function? f(x)=5(3)x-1
A.
B.
C.
D.
The graph of the function f(x) = 5(3)ˣ - 1 is represented as the diagram given in option C.
To find the main points of the function f(x) = 5(3)ˣ - 1, we can identify its key features such as the y-intercept, x-intercept, and any asymptotes.
Y-intercept:
To find the y-intercept, we set x = 0 and evaluate the function:
f(0) = 5(3)⁰ - 1 = 4
Therefore, the y-intercept is (0,4).
Asymptotes:
There are no vertical asymptotes for this function since the base of the exponential function, 3, is positive.
The graph of the function is given in the attached image.
Therefore, the correct option is C.
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employees receive a 10% discount their shopping at Tesco stores. calculate the weekly benefit to an employee who on average spend£14 each weekday and £22 on each day at the weekend.
The weekly benefit of the employees is A = £ 11.40
Given data ,
Let's calculate the weekly benefit for an employee who spends an average of £14 each weekday and £22 on each day of the weekend, considering the 10% discount they receive at Tesco stores.
First, we'll calculate the total amount spent on weekdays and weekends separately:
Amount spent on weekdays = £14/day x 5 days/week = £70/week
Amount spent on weekends = £22/day x 2 days/week = £44/week
Next, we'll calculate the total amount spent in a week by adding the amounts spent on weekdays and weekends:
On simplifying the equation , we get
Total amount spent in a week = £70 + £44 = £114
Now, we'll calculate the 10% discount on the total amount spent:
10% of £114 = £11.40
Hence , the weekly benefit to the employee who receives a 10% discount on their shopping at Tesco stores would be £11.40
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