Answer:
A polynomial's degree is the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients)
Step-by-step explanation:
The degree of a polynomial is the exponent of the leading term. For example, (x + 1) is a first-degree polynomial because x has an exponent of 1. (x^5 + 2y^4 - 3y^3 + y^2 - x + 3) is a fifth-degree polynomial because x has an exponent of 5.
The PTA sold 460 t-shirts on Friday
and 310 on Saturday. How many t-shirts did
they sell in all?
Solve the equation for all real solutions. --d2 - 12d + 4 = -6d?
the real solutions for the equation d² - 12 d + 4 = 6 is d = 6 ± √38.
The equation given is:
d² - 12 d + 4 = 6
Subtract 6 from both the sides:
d² - 12 d + 4 - 6 = 6 - 6
d² - 12 d - 2 = 0
solve for the real solutions:
D = b² - 4ac
D = (-12)² - 4(-2)(1)
D = 144 + 8
D = 152
d = 12 ±√152 / 2 (1)
d = 6 ± √38
Therefore, we get that, the real solutions for the equation d² - 12 d + 4 = 6 is d = 6 ± √38.
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Forearm lengths of men, measured from the elbow to the middle fingertip, are normallydistributed with a mean 18.8 inches and a standard deviation 1.1 inches.If 1 man is randomly selected, what is the probability that his forearm length is below 17
Solution
Part A
What are the parameters?
The parameters are
[tex]\begin{gathered} \operatorname{mean}\text{ = }\mu=18.8 \\ \text{Standard Deviation = }\sigma=1.1 \end{gathered}[/tex]We want to find
[tex]p(\mu<17)[/tex]Part B
Find the z score
The formula to use is given by
[tex]z=\frac{\bar{X}-\mu}{\sigma}[/tex][tex]\begin{gathered} z=\frac{\bar{X}-\mu}{\sigma} \\ z=\frac{17-18.8}{1.1} \\ z=\frac{-1.8}{1.1} \\ z=-1.6363636363 \\ z=-1.64 \end{gathered}[/tex]The construction of the standard normal curve is shown below
Part C
We use the standard normal table (from statistical table)
Thus, From statistical table
[tex]p(z<-1.64)=0.05[/tex]
In a sock drawer there are 8 black socks, 4 red socks and 6 orange socks, none of which are kept in a pair.
What is the probability that you will pull one red sock and one orange sock from the drawer with your first two random selections from the drawer?
Show your answer as decimal number, to two decimal places.
The probability that you will pull one red sock and one orange sock from the drawer will be 0.074, then the decimal number is 0.074.
Its fundamental tenet is that something almost probably will occur. the proportion of positive occurrences to all occurrences. The probability is then stated as,
What is a Probability :Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.
Probability = (Favorable event) / (Total event)
There are 8 black socks,
4 red socks, and
6 orange socks, every one of which is kept individually in a sock basket.
The total number of events will be,
Total number of events = 8 black socks + 4 red socks + 6 orange socks
Total number of events = 18 socks
The probability that you will pull one red sock and one orange sock from the drawer will be given as,
P = (4/18) x (6/18)
P = (2/9) x (6/18)
We can divide the numbers,
P = (2/9) x (1/3)
We can multiply the numbers,
P = 2/27
P = 0.074
Therefore,
The probability that you will pull one red sock and one orange sock from the drawer will be 0.074, then the decimal number is 0.074.
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Find the range of the function Find the x and y intercepts
For the function f(x) to be greater than 0 (f(x) > 0), we need to identify those regions strictly above the x-axis.
From the graph, these regions are (in interval notation):
[tex]\begin{gathered} R_1=(-6,-1) \\ \\ R_2=(4,6\rbrack \end{gathered}[/tex]For each region there is an inequality:
[tex]\begin{gathered} R_1:-6\lt x\lt-1 \\ \\ R_2:4\lt x\leqslant6 \end{gathered}[/tex]The domain is the set of x-values the function takes. Then, from the graph, we can see that the function is defined from x = -7 to x = 6. The domain of f(x) is:
[tex]Dom_f={}\lbrace x|-7\leqslant x\leqslant6\rbrace[/tex]The range is the set of y-values the function takes. From the graph, we see that the function has a minimum of -8 and a maximum of 12. Then, the range is:
[tex]Ran_f={}\lbrace y|-8\leqslant y\leqslant12\rbrace[/tex]For the x-intercepts (points with y = 0), we have:
[tex]-6,-1,4[/tex]For the y-intercept (the point with x = 0):
[tex]-4[/tex]marilee plants a vegetable patch measuring 12 m x 8 m .she plants carrots on half of the patch ,and potatoes on a quarter of the patch each .Calculate the area covered by each type of vegetable?
The area covered by each type of vegetables is 48 meter square and 24 meter square.
What is Area of rectangle?
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.
Area of rectangle = length × breadth
Total Area of rectangle = 12(8) = 96
Half area covered by carrots,
area of carrots patch = 96/2 = 48
area covered by potatoes = 96/4 = 24
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Sal's pizzeria charges
$414 for 23 pizzas. What
does the pizzeria charge
for one pizza?
Answer: 18 Dollars
Step-by-step explanation:
Divide 414 by 23 to get the cost per pizza. Which in this case is 18 dollars
Tom deposits $5,600 into a savings account. The simple interest rate for the account is 9.5%. If Tom does not withdraw any money from the account, how much money will be in the account after 3 years?
The amount of money in the account of Tom after 3 years with simple interest of 9.5 % is $6135.
What is simple interest?
Calculating the amount of interest that will be charged on a loan can be done quickly and easily using the simple interest formula. To calculate the simple interest, we need to multiply the principle amount, the number of days between payments (in years), and the interest rate (in decimals).
The formula to calculate Simple Interest is:
[tex]S. I. = P \times I \times T[/tex]
Here, P = Principal amount, I = interest rate (in decimals), T = time duration (in years).
putting the values from question:
[tex]S. I. = 5600 \times 0.095 \times 3[/tex]
Simple Interest = 535
The money in the account will be the sum of principal amount and the simple interest.
Final amount = Principal amount + Simple Interest.
A = 5600 + 535
A = 6135
Therefore, the money in the account after 3 years is $6135 .
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A. 1/3 x +y=72x + 6y = 12Questions What’s the slope Y intercept?Number of solutions?
To identify the slope (m) and y-intercept (b) you write each equation in slope intercept form by solving for y:
[tex]y=mx+b[/tex]First equation:
Substract 1/3 x in both sides of the equation:
[tex]\begin{gathered} \frac{1}{3}x-\frac{1}{3}x+y=-\frac{1}{3}x+7 \\ \\ \\ y=-\frac{1}{3}x+7 \end{gathered}[/tex]Slope: -1/3
Y-intercept: 7
Second equation:
Substract 2x in both sides o
[tex]undefined[/tex]commercials is a average of 16 minutes and a standard deviation equals 2.1 minutes. After watching the chanel for a hour randomly you observe the amount of commercials equals to 19 minutes Find the z score for the amount of commercials, round 2 decimals
To answer this question we will use the following formula to compute the z-score:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ \text{where x is the observed value, }\mu\text{ is the mean, and }\sigma\text{ is the standard deviation.} \end{gathered}[/tex]Substituting x=19min, μ=16min, and σ=2.1min we get:
[tex]z=\frac{19\min -16\min }{2.1\min }\text{.}[/tex]Simplifying the above result we get:
[tex]z=\frac{3}{2.1}=\frac{10}{7}\approx1.43.[/tex]Answer: 1.43.
help me please
thank you
Answer:
Domain: A, [tex][1, \infty)[/tex]
Range: [tex][-4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
so I need help pls!
(3 1/2 + 17 1/5) - (11 3/5 + 2 1/3)
Answer:
The answer rounded would be 6.7 but it not rounded would be 6.766
Step-by-step explanation:
Answer:
6 23/30 or [tex]6 \frac{23}{30}[/tex]
Let me know if it's wrong and I'll fix it! ^^
Ordered PairsWhat color goes with the numbers. So there are 9 total
To know the coordinates of each color, locate the y and the x coordinate.
The x- coordinate is where the point corresponds to the horizontal line. It is always written first.
The y-coordinate is where the point correponds to the vertical line.
The corrdinates are in the form of ordered pairs:
(x, y)
Use the given conditions to write an equation for the line in point slope form and slope intercept form. Passing through (-2,1) and parallel to the line whose equation is x-3y=5
The given point is (-2,1) and the given line is x-3y=5.
The slope of the given line can be determined as,
[tex]m=-\frac{1}{-3}=\frac{1}{3}[/tex]The equation of the line which is parallel to the given line will have the same slope.
Thus, the equation of the new line passing through (-2,1) can be determined as,
[tex]\begin{gathered} \frac{y-1}{x-(-2)}=\frac{1}{3} \\ 3(y-1)=x+2 \\ 3y-3=x+2 \\ 3y=x+5 \\ y=\frac{x}{3}+\frac{5}{3} \end{gathered}[/tex]Thus, the equation of the line in slope intercept form is y=x/3+5/3.
The equation of the line in the point slope form can be determined as,
[tex]\begin{gathered} (y-1)=\frac{1}{3}(x-(-2) \\ (y-1)=\frac{1}{3}(x+2) \end{gathered}[/tex]Thus, the equation of the line in the point slope form is (y-1)=(x+2)/3
so the answer is y-1=5/3
ငါထင္ပါတယ္။
given the continuous function, determine how many inflection points would be found on the graph. show the approximate location of each estimate.
inflection points are where there is a change of concavity:
What is the volume of the following prism?this is a prism with a triangular base. The width of the triangle is 6 meters and the height of the triangle is 3 meters. The height of the prism is 7 meters.A. 63 m³B. 189 m³C. 42 m³D. 126 m³
Answer
A. 63 m³
Explanation:
The volume of the prism is equal to
V = Bh
Where B is the area of the base and h is the height of the prism.
In this case, the base is triangular, so the area of the base is equal to
[tex]\begin{gathered} B=\frac{base\cdot height}{2} \\ \\ B=\frac{6\text{ m}\cdot3m}{2} \\ \\ B=\frac{18\text{ m}^2}{2} \\ \\ B=9\text{ m}^2 \end{gathered}[/tex]Then, the volume of the prism is equal to
V = (9 m²)(7 m)
V = 63 m³
Therefore, the answer is
A. 63 m³
Directions:Fill ih the missing measures.(parallelogram)Area:_Base: 7.4mHeight:9.3m
The formula for the area of parallelogram is,
[tex]A=bh[/tex]Here, b is base and h is height.
Determine the area of parallelogram for b = 7.4 and h = 9.3 m.
[tex]\begin{gathered} A=7.4\cdot9.3 \\ =68.82 \end{gathered}[/tex]So area is 68.82 meter square.
Triangle EFG is translated 3 units to the left. Then the image is dilated by a scale factor of 0.5 to form triangle E''F''G''. The center of dilation is the origin. Vertex E is located at (5, -6). What are the coordinates of vertex E''?
After a translate of 3 units to the left and dilation by a scale factor of 0.5, the coordinate of vertex E'' is (1, -3).
What is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.
Next, we would translate vertex E 3 units to the left by subtracting "3" from the x-coordinate as follows:
Vertex E = (5, -6) → Vertex E" = ((5 - 3), -6) = (2, -6).
Also, we would dilate the image E" by a scale factor of 0.5 as follows:
Vertex E" = (2 × 0.5, -6 × 0.5) → Vertex E" = (1, -3)
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A survey that 73% of adults need correction (eyeglasses, contacts, surgery, etc,) for their eyesight. If 20 adults are randomly selected, find the probability that no more than 1 of them need core for their eyesight. Is 1 a significantly low number of adults requiring eyesight correction?
The odds of there being less than one of them who needs glasses are extremely near to zero, the number one is considered to be a very low quantity.
This is further explained below.
What is a Binomial?Generally, Let X be the number of adults among 16 that needs correction. Then X ~ Binomial(n = 20, p = 0.73)
The probability that no more than 1 of them needs correction for their eyesight = P(X \le 1)
= P(X = 0) + P(X = 1)
[tex]= ^{20}C_0 * 0.73^0 * (1 - 0.73)^{20-0} + ^{20}C_1 * 0.73 * (1 - 0.73)^{20-1}[/tex]
= 2.33465379×10−10
= 0.000
The likelihood that no more than 1 of them require eyeglasses is close to 0, therefore 1 is a very low number.
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(a)Linda owns 28 shares of a certain stock. Yesterday the value of each share went up by 4 dollars. What was the total change in value of her shares?
The total change in the value of the shares is $112
Number of shares owned by Linda = 28 shares
The term "value change" describes the adjustment made to the share price to reflect the total number of issued and held by investors shares that are now outstanding. Investors' daily holdings of shares are influenced by changes in supply and demand, which can be periodically changed to keep up with the changes.
Increase in value of each share = $4
The total increase in value of shares = Number of shares*Increase in value of each share
= 28*4
So, the total increase in the shares = $112
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Felix exercises by spending 12 minutes warming up and then running for 20 minutes he has exercised a total of 240 minutes this mouth
Based on the number of minutes that Felix takes to exercise and the minutes he takes to warm up, the equation given does not describe the statement.
How to describe the statement as an equation?The number of minutes that Felix spends exercising and the number of minutes he spends running, should be added together to find the number of minutes Felix spends exercising in one session.
This means that the total minutes for exercising is:
= 12 + 20
= 32 minutes per session
The number of sessions that Felix exercised to get to a total of 240 minutes is therefore:
Number of minutes per session x Number of sessions = 240 minutes
Assuming the number of sessions is x, the equation would be:
32 × x = 240
32x = 240
The given equation of 20 + 12x=240 is therefore not described by the statement.
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A company purchased a new truck at a cost of $72,000 on July 1, 2019. The truck is estimated to have a useful life of 5 years and a salvage value of $2,000. The company uses the straight-line method of depreciation. The book value of the truck on December 31, 2019 is:
A company purchased a new truck, then the book value of the truck on December 31, 2019 is $51,000, because the company uses the straight-line method of depreciation.
A company purchased a new truck at a cost = $72,000 on July 1, 2019.
Estimated to have a useful life time = 5 years
A salvage value = $2,000
The formula for depreciation expense, using straight line method is;
What is a depreciation expense :Depreciation expense is the cost of an asset that has been depreciated for a single period, and shows how much of the asset's value has been used up in that year. Accumulated depreciation is the total amount of depreciation expense that has been allocated for an asset since the asset was put into use.
Based on the given conditions, formulate :
= (Cost - Salvage value) / life time (Equation-1)
We consider,
Cost = $72,000
Salvage value = $2,000
Life time = 5 years
We can substitute this values in equation-1,
So,
We can write,
= ($72,000 - $2,000) / 5
= $70,000 / 5
= $14,000.
Therefore,
The book value of the truck on December 31, 2019 would be;
= (cost - book value x (difference of year + difference of months/total months))
= $72,000 - $14,000 × (1 + 6/12)
= $72,000 - $14,000 x (1+1/2)
= $72,000 - $14,000 x (1+0.5)
= $72,000 - $14,000 x 1.5
= $72,000 - $21000
= $51,000
Note that we arrived at the value of 6 because July to December is 6 months.
Therefore,
The book value of the truck on December 31, 2019 is $51,000, because the company uses the straight-line method of depreciation.
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help 50 points need help math 7
Answer:
-5v + 6.2w - 3
Step-by-step explanation:
- (5v - 6.2w) -3
= -5v + 6.2w - 3
How many solutions does the following function have? 2x^2-3x+1=0
The given expression is
[tex]2x^2-3x+1=0[/tex]Let's use the discriminant to know the number of solutions.
[tex]b^2-4ac[/tex]Where a = 2, b = -3, and c = 1.
[tex](-3)^2-4\cdot2\cdot1=9-8=1[/tex]This means the equation has two real solutions.Solve this system of equations byusing the elimination method.3x + 4y = 4-X – 3y = 7=\וז ו7ro
Given:
System of equation is given as
[tex]\begin{gathered} 3x+4y=4 \\ -x-3y=7 \end{gathered}[/tex]Required:
Solve system of equation by using the method elimination.
Explanation:
By using the elimination method
we multiply second equation with 3 and then add in first equation
because by doing this process we eliminate the x
[tex]\begin{gathered} 3x+4y+3(-x-3y)=4+3*7 \\ 3x+4y-3x-9y=4+21 \\ -5y=25 \\ y=-5 \end{gathered}[/tex]now put the value of y in first equation
[tex]\begin{gathered} 3x+4(-5)=4 \\ 3x-20=4 \\ 3x=20+4 \\ 3x=24 \\ x=8 \end{gathered}[/tex]Final answer:
Solution of given system of equation is (8,-5)
The half life of Pb-210 is 22 years. A decayed animal shows 48% of the original Pb-210 remains; how long has the animal been deceased to the nearest tenth of a year?A .0.01 yearsB. 23.3 yearsC. 0.04 yearsD. 23.29 years
SOLUTION:
Step 1:
In this question, we are given the following:
The half-life of Pb-210 is 22 years.
A decayed animal shows 48% of the original Pb-210 remains;
how long has the animal been deceased to the nearest tenth of a year?
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} From\text{ the question, we can see that:} \\ 0.\text{ 5 = e}^{22k} \\ Making\text{ k the subject of the formulae, we have that:} \\ k\text{ = \lparen}\frac{ln\text{ 0. 5}}{22})\text{ --- equation 1} \end{gathered}[/tex][tex]\begin{gathered} \text{0. 48 = e}^{(\frac{I\text{n 0. 5}}{22})t} \\ Taki\text{ng In of both sides, we have that:} \\ ln\text{ \lparen0. 48 \rparen= \lparen}\frac{ln\text{ 0. 5}}{22}\text{ \rparen t} \end{gathered}[/tex][tex]Multiply\text{ both sides by \lparen}\frac{22}{ln\text{ 0. 5 }})\text{ , we have that:}[/tex][tex]\begin{gathered} \text{t = \lparen ln 0.48 \rparen }\times\text{ \lparen}\frac{22}{ln\text{ 0. 5 }}) \\ t=\text{ 23.29566} \\ t\approx\text{ 23.29 years \lparen OPTION D \rparen} \end{gathered}[/tex]
CONCLUSION:
The final answer is:
[tex]\text{t }\approx\text{ 23. 29 years \lparen OPTION D \rparen}[/tex]in the triangles below, m
In the given triangles,
∠B = ∠A
∠T = ∠M
Since, two angles of a triangle are equal, the third angle will also be equal.
Also, ΔLBT is similar to ΔHAM ........(by Angle - Angle similarity)
Now,
⇒ LB/HA = BT/AM = LT/HM ..........(Sides of similar triangles are proportional)
⇒ LB/HA = BT/AM
⇒ 4/HA = 6/10
⇒ 10 x 4 = HA x 6
⇒ HA = 40/6
⇒ HA = 20/3
⇒ HA = 6 2/3
What are Similar Triangles?Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size. Triangle resemblance is shown by the symbol ~ in this case.It is possible to prove that the corresponding sides of two triangles with congruent angles (also known as equiangular triangles) are proportionate. The AAA Similarity Theorem refers to this.Numerous synthetic (coordinate-free) Euclidean geometry proofs are based on similar triangles.The angle bisector theorem, geometric mean theorem, Menelaus' theorem, and Pythagorean theorem are only a few examples of basic conclusions that can be proven in this fashion. The fundamentals of right triangle trigonometry are also provided by similar triangles.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation: get smarter
HELP PLEASEEEEEEEEEEE!! ILL MARK BRAINLIEST
Answer:no 3*little5 is not same as 5*little3
Step-by-step explanation:3*little5 is 3x3x3x3x3,5*little3 is 5x5x5
Answer:
They are DIFFERENT.
Step-by-step explanation:
3^5 (exponential form) means
3×3×3×3×3 (this is the repeated multiplication)
So the standard form is 243.
The other term is:
exponential: 5^3
rep mult.: 5×5×5
standard form: 125
243 NotEqual 125
They are not the same. 3^5 and 5^3 are different.
What is the range for the distance between A and C
The range of distance from A to C is greater than 12.3 feet and less than 32.1 feet.
What is the Triangle inequality Theorem?To precisely state the dimensions of a triangle's sides, the triangle inequality theorem is a crucial component of geometry.
According to this rule, a triangle's third side must be longer than the sum of its other two sides.
Say, AB, BC, and CA make up three of the sides of the triangle ABC.
The length of (AB + BC) must therefore be longer than CA according to the triangle inequality theorem.
As a result, CA > (AB + BC).
The sum of the lengths of BC and CA must exceed the length of AB.
As a result, AB > (BC + CA).
The sum of the lengths of AB and CA must exceed the length of BC.
Consequently, (AB + CA) > BC.
As per the question:AB = 22.2 feet
BC = 9.9 feet
Taking AB as the longest side of the triangle.
The measure of AB must be less than the sum of AC and BC.
⇒ AC < AB + BC
⇒ AC < 22.2 + 9.9
⇒AC < 32.1 feet
Therefore, the range of distance from A to C is greater than 12.3 feet and less than 32.1 feet.
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