Maria's deal is a better deal
Explanations:First Deal: Martha sells apples in 5 lb bags for $4.00
Price of a 5 lb bag of apples = $4
Price of a 1 lb of apples = $4 /5 = $0.8
Second deal: Steve sells apples in 3 lb bags for $2.25
Price of a 3 lb bag of apples = $2.25
Price of 1 lb of apples = $2.25 / 3 = $0.75
The deal with the highest price per pound is the better deal
Maria sells at a higher price per pound than Steve, therefore, Maria's deal is better
if the point is on the unit circle what is X
The question can be represented by:
where
[tex]y=\frac{\sqrt[]{3}}{2}[/tex]Note that the Hypotenuse is 1 because a unit circle has a radius of 1.
Considering the triangle from the diagram above, we can find x using the Pythagorean Theorem:
[tex]\begin{gathered} 1^2=x^2+y^2 \\ 1=x^2+(\frac{\sqrt[]{3}}{2})^2 \\ 1=x^2+\frac{3}{4} \end{gathered}[/tex]Solving for x, we have
[tex]\begin{gathered} x^2=1-\frac{3}{4} \\ x^2=\frac{1}{4} \\ x=\sqrt[]{\frac{1}{4}} \\ x=\frac{1}{2} \end{gathered}[/tex]The value of x is 1/2.
Law of Sines; B ≈ 42.7°, C ≈ 102.3°, c ≈ 18.7Law of Sines; B ≈ 102.3°, C ≈ 42.7°, c ≈ 18.7Law of Cosines; B ≈ 106.2°, C ≈ 38.8°, c ≈ 18.7Law of Cosines; B ≈ 38.8°, C ≈ 106.2°, c ≈ 18.7
The sine rule is used when we are given either
a) two angles and one side, or
b) two sides and a non-included angle.
The cosine rule is used when we are given either
a) three sides or
b) two sides and the included angle.
For the given problem, we are given a non-included angle and two sides. Hence, we have to solve the problem using the law of sines.
The sine rule states that:
[tex]\frac{\sin\text{ A}}{a}\text{ =}\frac{\sin\text{ B}}{b}\text{ }[/tex]We have:
A = 35 degrees, b = 13, a = 11
Substituting we have:
[tex]\begin{gathered} \frac{\sin35^0}{11}=\text{ }\frac{\sin \text{ B}}{13} \\ \text{Cross}-\text{Multiply} \\ \sin \text{ B }\times11=sin35^0\times13 \end{gathered}[/tex]Divide both sides by 11 and solving for B:
[tex]\begin{gathered} \sin \text{ B = }\frac{\sin \text{ 35 }\times13}{11} \\ \sin \text{ B = 0.677863} \\ B\text{ = 42.68} \\ \approx\text{ 42.7} \end{gathered}[/tex]Using the property of triangles, we can find the angle C:
[tex]\begin{gathered} \angle\text{ A + }\angle\text{ B + }\angle\text{ C =180 (sum of angles in a triangle)} \\ \angle\text{ C = 180 - 42.7 - 35} \\ \angle C\text{=1}02.3 \end{gathered}[/tex]Using the sine rule, we can solve for the unknown side c. We have:
[tex]\begin{gathered} \frac{\sin\text{ C}}{c}=\text{ }\frac{\sin \text{ B}}{b} \\ \frac{\sin\text{ 102.3}}{c}=\text{ }\frac{\sin \text{ 42.7}}{13} \\ \text{Cross}-\text{Multiply} \\ c\text{ }\times\text{ sin 42.7 = sin 102.3 }\times\text{ 13} \\ c\text{ = }\frac{\sin \text{ 102.3 }\times13}{\sin \text{ 42.7}} \\ c\text{ = 18.7295} \\ c\text{ }\approx\text{ 18.7} \end{gathered}[/tex]Answer summary
Law of Sines; B ≈ 42.7°, C ≈ 102.3°, c ≈ 18.7
The diagram shows figures that are squares and figures that are rhombi
• 4 sides
,• All sides congruent
,• Opposite sides parallel
,• Opposite sides congruent
1) Examining the squares and the rhombi we can state:
Squares
• 4 sides
,• All sides congruent
,• Opposite sides parallel
,• Opposite sides congruent
Rhombi
• 4 sides
,• All sides congruent
,• Opposite sides parallel
,• Opposite sides congruent
2) Then these are the answers above
what is 6x2/5 and 5x2/3 and 6x2/10
When multiplying fractions we need to multiply the numerator of one of the fractions by the numerator of the other and the denominator of one to the denominator of the other. This is done below.
[tex]6\cdot\frac{2}{5}=\frac{12}{5}[/tex][tex]5\cdot\frac{2}{3}=\frac{10}{3}[/tex][tex]6\cdot\frac{2}{10}=\frac{12}{10}=\frac{6}{5}[/tex]hi, can you help me answer this question, please, thank you:)
If the number of tablets in a shipment is sufficiently large, we can consider the testing procedure you describe (selecting a random sample of 21 ibuprofen tablets and counting the number of defective tablets in the sample) to be a binomial probability experiment.
Let X = (Number of defective ibuprofen tablets in a random sample of 21 tablets.) Then we may reasonably assume that X follows a binomial distribution. For each "trial" (that is, each tablet selected), there are two possible outcomes, "success" (the tablet is defective), or "failure" (the tablet is not defective).
Note that the word success as used in the binomial distribution does not carry the connotation of being a "good" outcome. A "success" is simply the outcome you are interested in counting, which in this case is the number of defectives in the sample.
The important parameters for a binomial distribution are n (the number of trials) and p (the probability of success on any one trial.)
For this situation, we have p= 0.01 (since we are told 1% of the tablets in the shipment are defective) and n = 21.
The general formula for the binomial distribution is
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]Where x is the number of successes in n trials (In this problem, x is the number of defectives in a random sample of 21 tablets.)
The symbol nCx is the "number of combinations of n things taken x at a time". This is the number ways of choosing x distinct objects from a set of n objects, without regard to order.
It is given by
[tex]^nC_x=\frac{n!}{x!(n-x)!}[/tex]where ! is the factorial symbol.
We want to find the probability that the shipment is accepted. We are told that a shipment will be accepted if at most one tablet doesn't meet the required specifications. That is, the number of defectives must be less than or equal to one.
P(Shipment accepted) = P(x ≤ 1). (In this case, x ≤ 1 if and only if x=0 or x=1) =P(0) + P(1)
So we calculate P(0) (the probability of 0 defective tablets in the shipment),
and P(1) (the probability of 1 defective.)
Using the formula for the binomial distribution, we have
[tex]\begin{gathered} P(0)=^{21}C_0(0.01)^0(1-0.01)^{21-0} \\ P(0)=\frac{21!}{0!(21-0)!}\times1\times0.99^{21} \end{gathered}[/tex][tex]\begin{gathered} P(0)=\frac{21!}{1\times21!}\times1\times0.809728 \\ P(0)=1\times1\times0.809728 \\ P(0)=0.809728 \end{gathered}[/tex][tex]\begin{gathered} P(1)=^{21}C_1(0.01)^1(1-0.01)^{21-1} \\ P(1)=\frac{21!}{1!(21-1)!}\times0.01\times0.99^{20} \end{gathered}[/tex][tex]\begin{gathered} P(1)=\frac{21!}{1\times20!}\times0.01\times0.817907 \\ P(1)=\frac{21\times20!}{20!}\times0.01\times0.817907 \\ P(1)=21\times0.00817907 \\ P(1)=0.171760 \end{gathered}[/tex]Finally, then, we have:
P(Shipment accepted)= P(0) + P(1)
[tex]\begin{gathered} P(0,1)=0.809728+0.171760 \\ P(0,1)=0.981488 \\ P(0,1)\approx0.9815(4decimal\text{ place)} \end{gathered}[/tex]Hence, the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 1% rate of defects is 0.9815 corrected to 4 decimal places
a.The amount of money invested in a retirement fund is an example of which of the followinginvestment assetb. liquid assetC. long term assetd. use asset
Answer:
It is an investment asset.
Step-by-step explanation:
It is an investment asset.
An investment asset are itens, tangible or intangible, that are used to produce additional income, or held based on speculation. Examples are mutual funds, stocks or retirement funds.
A leprechaun places a magic penny under a girl's pillow. The next night there are 2 magic pennies under her pillow. Each night the number of magic pennies doubles. How much money will the girl have after 25 nights?Question content area bottomHow much money will the girl have after 25 nights?
The given sequence are:
2, 4, 8, 16...
Here, first term(a) = 2, common ratio(r) = 2 and we find the 25th term.
Therefore, we know that the sequence formula is:
[tex]a_r=ar^{n-1}[/tex]Then, for the 25th term:
[tex]a_{25}=2\times2^{25-1}=2\times2^{24}=33554432[/tex]Total money in dollars:
[tex]33554432\times0.01=335544.32[/tex]Answer: the girl will have $335544.32
3. Jada's sister earns a commission. She makes 3.5% of the amount she sells. Last week, she sold $7,000 worth of furtniture. How much was her commission? (don't forget the $)
The commission made was $245 from the sales
Here, we want to get the value of the commission made
From the question, we are told that the commission is 3.5% of the amount sold
We have this as;
[tex]\frac{3.5}{100}\times\text{ 7000 = \$245}[/tex]list the 6 exponent rules with names and formulas
To list the 6 exponent rules with names and formulas.
Explanation:
The 6 exponent rules are,
1) Product with the same bases
[tex]a^m\times a^n=a^{m+n}[/tex]2) Quotient with same bases,
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]3) Power raised to a power.
[tex](a^m)^n=a^{mn}[/tex]4) Product to a power.
[tex]a^nb^n=(ab)^n[/tex]5) Quotient to a power
[tex]\frac{a^n}{b^n}=(\frac{a}{b})^n[/tex]6) Zero power
[tex]a^0=1[/tex]THE HYPOTHESIS RED AND THE CONCLUSIONIf the weather is cold and wet, then the season is winter.
In this problem
The Hypothesis is: The weather is cold and wet
The conclution: The season is winter
For the polynomial function below: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of |x|
ANSWER
[tex]\begin{gathered} x\text{ = 0 (multiplicity of 2)} \\ x\text{ = }\sqrt[]{7}\text{ (multiplicity of 1)} \\ x\text{ = - }\sqrt[]{7}\text{ (multiplicity of 1)} \end{gathered}[/tex]
EXPLANATION
[tex]\begin{gathered} f(x)=-7x^2(x^2-7) \\ \text{set }-7x^2(x^2-7)\text{ = 0} \\ x^2\text{ = 0} \\ x\text{ = +-}\sqrt[]{0} \\ x\text{ = 0}\ldots\ldots..\ldots..\ldots\ldots.(1) \\ x^2\text{ - 7 = 0} \\ x^2\text{ = 7} \\ x\text{ = +-}\sqrt[]{7} \\ x\text{ = }\sqrt[]{7}\text{ or x = -}\sqrt[]{7}\ldots\ldots\ldots....\ldots\ldots\text{....}\mathrm{}.(2) \end{gathered}[/tex]The final solution is all the values that make -7x^2(x^2 -7) = 0 true.
while the multiplicity of a root is the number of times the root appears.
for the multiplicity:
[tex]\begin{gathered} x\text{ = 0 (multiplicity of 2)} \\ x\text{ = }\sqrt[]{7}\text{ (multiplicity of 1)} \\ x\text{ = - }\sqrt[]{7}\text{ (multiplicity of 1)} \end{gathered}[/tex]What is the value of 1 unit as a fraction?
The Solution:
From the given information in the picture.
Half of 10 units = 5 units
[tex]\frac{1}{2}of\text{ 10}=\frac{1}{2}\times10=5\text{ units}[/tex]We are asked to find the value of 1 unit as a fraction.
That is one unit out of ten units.
[tex]1\text{ unit =}\frac{1}{10}[/tex]Thus, the correct answer is
[tex]\frac{1}{10}[/tex]What is the GCF of 12a^5 and 38a^4b^2
Given:
There are give that the expression:
[tex]12a^5,and,38a^4b^2[/tex]Explanation:
According to the question:
We need to find the value of GCF.
So,
For the GCF:
Find the prime factors of each term in order to find the greatest common factor (GCF).
Then,
From the expression:
[tex]\begin{gathered} 12a^5\rightarrow2\times2\times3\times a\times a\times a\times a\times a \\ 38a^4b^2\rightarrow2\times19\times a\times a\times a\times a\times b\times b \end{gathered}[/tex]Then,
[tex]\begin{gathered} 12a^5\operatorname{\rightarrow}\times2\times2\times3\times a\times a\times a\times a\times a \\ 38a^4b^2\operatorname{\rightarrow}\times2\times19\times a\times a\times a\times a\times b\times b \\ =2a^4 \end{gathered}[/tex]Final answer:
Hence, the value of GCF is shown below:
[tex]\begin{equation*} 2a^4 \end{equation*}[/tex]INEQUALITIESTranslation: A minimum number of 17Translation: A minimum number that is at least 90
The first statement is "A minimum number of 17". This can be expressed as
[tex]x<17[/tex]The second statement is "A minimum number that is at least 90". This can be expressed as
[tex]x\ge90[/tex]what are the experimental units in this setting?A. the types of detergent B. the 10 loads of shirtsC. the volunteers who assess the stainsD. the machines used to wash the shirts
Answer:
B
Step-by-step explanation:
I just took the quiz.
The expression -120+13m represents a submarine that began at a depth of 120 feet below sea level and ascended at a rate of 13 feet per minute. (m). Write an expression that could be used to describe the situation.
h = -120 + 13m This is the expression that they ask you for.
The solution was given in the problem.
How many solutions does this equation have?4 - 8V = 10 – 8v
4 - 8V = 10 – 8v
Collect like terms
8v - 8v = 10 - 4
The equation has no solution
Henry stores the arrowheads he has found in a box the shape of a rectangular prism. The box is 14 inches long, 12 inches wide and 2 inches high. He plans to paint the exterior of the box. How many square inches does he have to paint? 2 in. 14 in. 12 in.
Side areas
The box in the image has six sides, each one consisting of rectangles
Note the sides come in pairs of equal areas
For example, the front and the back sides have the same dimensions, thus their areas are equal. Let's calculate them
Area of front side = 12 in * 2 in = 24 square inches
The sum of the front and back areas is:
2 * 24 = 48 square inches
Now for the lateral sides. Again, we have two similar shapes with identical areas:
Area of one lateral side = 14 in * 2 in = 28 square inches
Area of both lateral sides = 2 * 28 = 56 square inches
Finally, the top and bottom areas are equal:
Area of top side = 12 in * 14 in = 168 square inches
Area of top and bottom sides = 2* 168 = 336 square inches
The total area is
48 + 56 + 336 = 440 square inches
Henry has to paint 440 square inches
Rewrite the following in logarithmic form:a) 6 to 3rd power (sorry my superscript short cut isn't working) = 216b) 10 to the 0 power =xc) e to the x power =28
Part a
we have
[tex]6^3=216[/tex]so
in logarithmic form
[tex]\log _6216=3[/tex]Part b
[tex]10^0=x[/tex]in logarithmic form
[tex]\begin{gathered} \log _{10}x=0 \\ \log x=0 \end{gathered}[/tex]Part c
we have
[tex]e^x=28[/tex]in logarithmic form
[tex]\ln 28=x[/tex]Joanna is wrapping a present in the box shown. Find the amount of wrapping paper in square inches that Joanna needs, not counting overlap.
Recall
[tex]1\text{ foot = 12inches}[/tex]Given parameters
Length =12inches
Breadth = 8inches
Height =6 inches
Step 1
Formula
The total surface area of a cuboid
[tex]\text{The total surface area }of\text{ a cuboid =2(lb+bh+hl)}[/tex]Step 2
Substitute the given parameters
[tex]\begin{gathered} \text{The total surface area }of\text{ a cuboid =2((}12\times8)\text{+(8}\times6)\text{+(6}\times12)\text{)} \\ \text{The total surface area }of\text{ a cuboid =2((96})\text{+(48})\text{+(72})\text{)} \\ \text{The total surface area }of\text{ a cuboid =2(216)} \\ \text{The total surface area }of\text{ a cuboid =}432in^2 \end{gathered}[/tex]The final answer
The amount of wrapping paper that Joanna needs is 432 square inches
What is the Subtraction Property of Equality? Use the Subtraction Property of Equality to complete to following statement: If 10x + 6 = 21, then ____ = 15
The subtraction property of equality allows us to subtract the same number from both sides of an equation preserving its validity.
For example, the equation x + 2 = 3 can be subtracted 1 and obtain x + 1 = 2
We are given the equation:
10x + 6 = 21
We need to subtract a number in such a way that the 21 turns into a 15.
That number is 6, thus, subtracting 6 on both sides:
10x = 15
The missing expression is 10x as underlined above.
Use parallelogram to find
Take into account that the measure of the angle XYZ is the same that angle ZWY:
m∠XYZ = M∠ZWY = 105°
next, consider the sum of the interior angles of the parallelogram is 360°, moreover, angle WZY and angle WXY are congruent.
Then, you have:
2m∠XYZ + 2m∠WZY = 360°
solve the previous equation for m∠WZY:
2m∠WZY = 360 - 2m∠XYZ
2m∠WZY = 360 - 2(105)
2m∠WZY = 360 - 210
2m∠WZY = 150
m∠WZY = 150/2
m∠WZY = 75
Hence, the measure of the angle WZY is 75°
In 2003, the population of an African country was about 20 million people, which is 2 million more than 4times the population in 1950.Enter and solve an equation to find the approximate population p (in millions) in 1950.An equation isThe approximate population in 1950 wasmillion people.
We know that
• African country was about 20 million people, in 2003.
,• Which is 2 million more than 4 times the population in 1950.
I need help this question and I need the answer asap please
Answer:
what is the question?
Step-by-step explanation:
what is the question?
The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 16 cm and a second side that is 2 cm less than twice the third side, what are the possible lengths for the second and third sides?
We are given that the sum of the lengths of any two sides of a triangle must be greater than the third side
To find the possible lengths for the second and third sides, we will make an assumption below.
Let the third side be x
Since the second side is 2 cm less than twice the third side, this can be expressed as
[tex]\text{side 2=2x-2}[/tex]With this we can note that
side 1 = 16cm
side 2 =2x-2
side 3 = x
Going back to the initial rule that the sum of the lengths of any two sides of a triangle must be greater than the third side
We can sum any two sides and equate it to the third side.
[tex]\begin{gathered} \text{side}2+\text{side}3\text{ >side1} \\ 2x-2+x>16 \\ 3x>16+2 \\ 3x>18 \\ x>\frac{18}{3} \\ x>6 \end{gathered}[/tex]Since the third side is x therefore, the possible length of the third side is 6cm and above
ANSWER 1: third side= 7cm and above
Also, the second side is 2x-2. We will use a minimum value of 6
[tex]\begin{gathered} \text{side 2 = 2x-2} \\ \text{side 2 = 2(}6\text{)}-2 \\ \text{side 2 =12-2} \\ \text{side 2 =10} \\ \\ \end{gathered}[/tex]ANSWER 2: the second side is 10cm and above
Find the length of the arc on a circle of radius r intercepted by a central angle ∅. 5. Radius, r = 12 inches Central Angle, ∅ = 45°
We are asked to find the length of the arc on a circle
Radius = r = 12 inches
Central Angle = θ = 45°
The arc length on a circle is given by
[tex]arc=2\cdot\pi\cdot r(\frac{\theta}{360\degree})[/tex]Let us substitute the given values of r and θ
[tex]\begin{gathered} arc=2\cdot\pi\cdot r(\frac{\theta}{360\degree}) \\ arc=2\cdot\pi\cdot12(\frac{45\degree}{360\degree}) \\ arc=24\cdot\pi(\frac{1\degree}{8\degree}) \\ arc=\frac{24\cdot\pi}{8} \\ arc=3\pi \end{gathered}[/tex]Therefore, the arc length is found to be 3π inches.
Solving systems x=-2y+1. 4=x+y
Answer:
(x, y) = (7, -3)
Explanation:
Given the syatem of equations:
x=-2y+1 ... 1
4=x+y ... 2
Substitute equation 1 into 2:
4 = -2y+1+y
4 = -2y+y+1
4 = -y+1
-y = 4-1
-y = 3
y = -3
Substitute y = -3 into equation 1:
x = -2y+1
x = -2(-3)+1
x = 6+1
x = 7
Hence the solution to the system of equations is (7, -3)
Ganjina buys 5 pounds of turkey for $21.25. How much does she pay per ounce? * 1 pound = 16 ounces
To find the answer to this question, we need to convert 5 pounds into ounces:
[tex]5lb\cdot\frac{16ounce}{1lb}=80\text{ounces}[/tex]Then, we need to divide the total price by the total ounces:
[tex]\frac{21.25}{80}=0.265\approx0.27[/tex]Then, Ganjina pays $0.27 per ounce or 27 cents per ounce.
Find the midpoint of points A (2,4) and B(-2,9) graphically
To find the midpoint of points A and B graphically, we need to start by drawing the given points.
A(2,4) and B(-2,9).
The graph looks like this:
To find the coordinates of the midpoint, add the x-coordinates and divide by 2, and do the same for the y-coordinates, then:
[tex]\text{Midpoint: (}\frac{2+(-2)}{2},\frac{4+9}{2})=(\frac{0}{2},\frac{13}{2})=(0,6.5)[/tex]Thus, the midpoint is at (0,6.5). In the graph it is at:
a chef is going to use a mixture of two brands of Italian dressing. the first brand contains 5% vinegar, and the second brand contains 8% vinegar. the chef wants to make 300 milliliters of a dressing that is 6% vinegar. how much of each branch should she use?First brand: __milliliters Second brand: __milliliters
Let A be the first brand and B the second brand, then, we can write
[tex]\begin{gathered} 0.05A+0.08B=0.06\times300\ldots(a) \\ \text{and} \\ A+B=300\ldots(b) \end{gathered}[/tex]so we have 2 equations in 2 unknows.
Solving by substitution method.
By moving B to the right hand side in the second equation, we have
[tex]A=300-B\ldots(c)[/tex]By substituting this result into equation (a), we have
[tex]0.05(300-B)+0.008B=18[/tex]where 18 = 0.06x300. By combining similar terms, we get
[tex]\begin{gathered} 15-0.05B+0.08B=18 \\ 15+0.03B=18 \end{gathered}[/tex]By moving 15 to the right hand side, we obtain
[tex]\begin{gathered} 0.03B=18-15 \\ 0.03B=3 \end{gathered}[/tex]then, B is equal to
[tex]\begin{gathered} B=\frac{3}{0.03} \\ B=100 \end{gathered}[/tex]Now, by substituting this result into equation (c), we have
[tex]\begin{gathered} A=300-100 \\ A=200 \end{gathered}[/tex]This implies tha the answer is:
First brand: 200 mililiters
Second brand: 100 mililiters