Answer:
f=-x^2/2-2
Step-by-step explanation:
(1 point) Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7. 257 (b) are divisible by 5 but not by 7. (c) are divisible by 5. (d) are divisible by 7.
Using arithmetic sequences, it is found that there are:
a) 257 numbers that are are divisible by 5 and by 7.
b) 1543 numbers that are divisible by 5 but not by 7.
c) 1800 numbers that are divisible by 5.
d) 1286 numbers that are divisible by 7.
In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term.
Item a:
Numbers that are divisible by 5 and 7 are multiples of 35, as the least common multiple of 5 and 7 are 35, thus we have an arithmetic sequence with [tex]d = 35[/tex].The first multiple of 35 in this interval is 1015, so [tex]a_1 = 1015[/tex].The last multiple of 35 in this interval is 9975, so [tex]a_n = 9975[/tex].We apply the general formula and solve for n, thus:
[tex]a_n = a_1 + (n-1)d[/tex]
[tex]9975 = 1015 + 35(n-1)[/tex]
[tex]35n - 35 = 8960[/tex]
[tex]35n = 8995[/tex]
[tex]n = \frac{8995}{35}[/tex]
[tex]n = 257[/tex]
There are 257 numbers that are are divisible by 5 and by 7.
Item b:
First, we find the number of multiples of 5, with [tex]a_1 = 1000, a_n = 9995, d = 5[/tex]. Thus:
[tex]a_n = a_1 + (n-1)d[/tex]
[tex]9995 = 1000 + 5(n-1)[/tex]
[tex]5n - 5 = 8995[/tex]
[tex]5n = 9000[/tex]
[tex]n = \frac{9000}{5}[/tex]
[tex]n = 1800[/tex]
Of those numbers, 257 are multiples of 35, which means that they also are multiplies of 7, thus they are removed.
1800 - 257 = 1543.
There are 1543 numbers that are divisible by 5 but not by 7.
Item c:
From the previous item, there are 1800 numbers that are divisible by 5.
Item d:
We find the number of multiples of 7, with [tex]a_1 = 1001, a_n = 9996, d = 7[/tex]. Thus:
[tex]a_n = a_1 + (n-1)d[/tex]
[tex]9996 = 1001 + 7(n-1)[/tex]
[tex]7n - 7 = 8995[/tex]
[tex]7n = 9002[/tex]
[tex]n = \frac{9002}{7}[/tex]
[tex]n = 1286[/tex]
There are 1286 numbers that are divisible by 7.
A similar problem is given at https://brainly.com/question/23901992
In 2000 pizza costs 7.50 and in 2015 it costs 9.00 what is the percentage of change in the cost of the pizza
Four people are painting a house
Rishi paints of the house, Monique paints 25% of the house, Haley paints 0.02 of
the house, and Diego paints 0.1 of the house.
1/8 -> 0.125
25% -> 0.25
0.02 -> 0.02
0.1 -> 0.10
least -> greatest
Haley, 0.02 -> Diego, 0.1 -> Rishi, 1/8 -> Monique, 25%
Arranging the persons from least to greatest
Haley < Diego < Rishi < Monique
What is fraction?A number expressed as a quotient, in which a numerator is divided by a denominator.
Given:
Rishi paints = 1/8 = 0.125
Monique paints = 0.250
Haley paints = 0.020
Diego paints = 0.100
Now, arranging the persons from least to greatest
Haley < Diego < Rishi < Monique
Learn more about fraction here:
https://brainly.com/question/10354322
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hello please help me
Answer:
perimeter is 9+7.5+6=22.5cmwe know that area is(1/2* base *height)=1/2*9*4.2
=18.9square cm
Answer:
Perimeter: 6 + 7.5 + 9 = 22.5
area: 18.9
Step-by-step explanation:
Find the slope of a line that passes through points (-1,-5) and (6,9).
Answer:
[tex]{ \rm{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \\ { \rm{slope = \frac{9 - ( - 5)}{6 - ( - 1)} }} \\ \\ { \rm{slope = \frac{14}{7} }} \\ \\ { \boxed{ \rm{ \: \: slope = 2 \: \: }}}[/tex]
Find the volume of the composite solid.
Answer:
The answer would be c
Step-by-step explanation:
Answer:
B, if not then it's D
Step-by-step explanation:
A fair die is rolled 10 times, what is the probability to get 4 ones.
Answer:
7/128
Step-by-step explanation:
Simplify the following:
add 4 1/2 + 1 2/5 pls help me its telling me to add extra words srryt
Answer:
5 9/10
Step-by-step
Have the fraction with common denominators: 5/10 and 4/10
PLEASE HELP ITS MATH THANK YOUUUU
The population of a certain inner-city area is estimated to be declining according to the model P(t)=184,000e^−0.012t, where t is the number of years from the present. What does this model predict the population will be in 6 years? Round to the nearest person.
__________ people
Answer:
EZ answer 9+10=21
Step-by-step explanation:
someone please help with this question for brainliest !!!!:)
Answer:
d)
Step-by-step explanation:
the polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial x-r is equal to f(r). In particular, x-r is a divisor (that means a factor) of f(x), if and only if f(r)=0.
our r here is -1 to get x + 1.
f(-1) = 2×(-1)³ + 5×(-1)² - -1 - 6 = -2 + 5 + 1 - 6 = -2
the remainder is -2.
and since the remainder is <> 0, the binomial cannot be a factor.
Solve for y.
y-x= 11
x= 12
y=
Answer:
y=23
Step-by-step explanation:
y-x=11
x=12
y=x+11
y=12+11
y=23
Kenji and Alec are making paper kites for a kite fight, Kenji's kite is a rectangle and Alec's kite is a
parallelogram that is not a rectangle. Each boy draws
a model of his kite on grid paper. Does Alec's kite use
more paper than Kenji's kite?
Answer:
No
Step-by-step explanation:
Kenji's kite uses more paper
with in the image below, disregarding the scale of the objects, which of the numbered sets of basic shapes are capable building the larger shape shown below? I II III IV Select the single best answer
Find the value of x
Write ur answer in simplest form
Answer:
x = 10
Step-by-step explanation:
a² + b² = c²
(5√2)² + (5√2)² = x²
50 + 50 = x²
x² = 100
x= 10
Write True or False for each statement.
(a) A square is a special rectangle.
true or false?
(b) The diagonals of a rhombus are equal in length.
true or false?
(c) A kite has both pairs of opposite angles equal.
true or false?
Answer:
A) true
B) true
C) true
hope that helps :)
helping with this question
Answer:
G. 5
Step-by-step explanation:
I've done this exam beofre
Write the equation in the standard linear equation form (Ax+By=C) if possible. Is the equation linear? y/3+x=5
Answer:
3x + y = 15
Step-by-step explanation:
y/3 + x = 5
You can first move the x and y variable around so it fits the standard linear equation format.
x + y/3 = 5
In order to make it look more like the standard format, you can multiply both sides of the equation by 3 to get rid of the 3 in the denominator of the y variable. It would look like this:
3 ( x +y/3) = 3 ( 5 )
When you multiply this out, you get this:
3x + y = 15
43% of a town has blue eyes, 46% has blonde hair, and 24% has both. What is the probability that a random person picked will have both?
Answer:
24 by 113
Step-by-step explanation:
43 + 46 + 24 = 113
the % of people with both is 24%, thus the answer will be 24 by 113
Hope its correct and helps ya :)
Need help with this tricky image
All the people of a neighborhood pooled together and won the lottery. They won $10,000,000 and each person got a 0.02 share. How much money did each person receive?
Answer:
$200,000
Step-by-step explanation:
They all won $10,000,000 and
each person got a 0.02 share of the $10,000,000
Each person received
10,000,000*0.02 = $200,000
please tell me how this done with steps so I can do this on my own as well
Answer:
6
Step-by-step explanation:
Because J is the midpoint of KL, it means that KJ ans JL are equal.
Think about it like this:
What is the midpoint (or halfway point) of 4 and 8? The answer is 6, you would do 4 + 8 which is 12 and divide it by 2. There is an equal distance of 2 between 4 and the midpoint, and midpoint and 8. In the same way, JL is also 6Hope this helps!
Step-by-step explanation:
the midpoint of a line splits the line into 2 equally long parts.
therefore, JI must be equally long to KJ.
x = 6
and with KJ = 6 and JI = 6, then KI = KJ + JI = 6+6 = 12
Alex‘s credit card balance is -$200 after a long she makes a payment of $50 towards her bill what integer represents
how much she still owes
Answer: 250
Step-by-step explanation:
i took a test
I need help with Part B does anybody know
Answer:
Ako pilipino
Step-by-step explanation:
I'm on american hehe pilipino talaga ako
please help with solving
Record the following data in the circle graph 25% of the people like science the best ,half of the people like math the best, 25% of the people like reading the best.
Answer:
ok so it would be square root 2
Step-by-step explanation:
trying to figure this out
Does anyone remember how to do domain and range?
Answer:
Ummm no not really
Step-by-step explanation:
Answer:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
The temperature was -6° Fat 8:00 AM, over the next 6 hours, the temperature rose 11°. What is the new temperature at 2 PM?
Answer:
5 degrees Fahrenheit
Step-by-step explanation:
-6 + 11 = 5